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https://www.ademcetinkaya.com/2023/03/bldr-builders-firstsource-inc-common.html
|
Outlook: Builders FirstSource Inc. Common Stock is assigned short-term Ba1 & long-term Ba1 estimated rating.
Dominant Strategy : Sell
Time series to forecast n: 15 Mar 2023 for (n+6 month)
Methodology : Ensemble Learning (ML)
## Abstract
Builders FirstSource Inc. Common Stock prediction model is evaluated with Ensemble Learning (ML) and Stepwise Regression1,2,3,4 and it is concluded that the BLDR stock is predictable in the short/long term. According to price forecasts for (n+6 month) period, the dominant strategy among neural network is: Sell
## Key Points
1. Why do we need predictive models?
2. Can neural networks predict stock market?
3. Technical Analysis with Algorithmic Trading
## BLDR Target Price Prediction Modeling Methodology
We consider Builders FirstSource Inc. Common Stock Decision Process with Ensemble Learning (ML) where A is the set of discrete actions of BLDR stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4
F(Stepwise Regression)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Ensemble Learning (ML)) X S(n):→ (n+6 month) $∑ i = 1 n r i$
n:Time series to forecast
p:Price signals of BLDR stock
j:Nash equilibria (Neural Network)
k:Dominated move
a:Best response for target price
For further technical information as per how our model work we invite you to visit the article below:
How do AC Investment Research machine learning (predictive) algorithms actually work?
## BLDR Stock Forecast (Buy or Sell) for (n+6 month)
Sample Set: Neural Network
Stock/Index: BLDR Builders FirstSource Inc. Common Stock
Time series to forecast n: 15 Mar 2023 for (n+6 month)
According to price forecasts for (n+6 month) period, the dominant strategy among neural network is: Sell
X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)
Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)
Z axis (Grey to Black): *Technical Analysis%
## IFRS Reconciliation Adjustments for Builders FirstSource Inc. Common Stock
1. An entity shall apply this Standard for annual periods beginning on or after 1 January 2018. Earlier application is permitted. If an entity elects to apply this Standard early, it must disclose that fact and apply all of the requirements in this Standard at the same time (but see also paragraphs 7.1.2, 7.2.21 and 7.3.2). It shall also, at the same time, apply the amendments in Appendix C.
2. However, the fact that a financial asset is non-recourse does not in itself necessarily preclude the financial asset from meeting the condition in paragraphs 4.1.2(b) and 4.1.2A(b). In such situations, the creditor is required to assess ('look through to') the particular underlying assets or cash flows to determine whether the contractual cash flows of the financial asset being classified are payments of principal and interest on the principal amount outstanding. If the terms of the financial asset give rise to any other cash flows or limit the cash flows in a manner inconsistent with payments representing principal and interest, the financial asset does not meet the condition in paragraphs 4.1.2(b) and 4.1.2A(b). Whether the underlying assets are financial assets or non-financial assets does not in itself affect this assessment.
3. If the group of items does not have any offsetting risk positions (for example, a group of foreign currency expenses that affect different line items in the statement of profit or loss and other comprehensive income that are hedged for foreign currency risk) then the reclassified hedging instrument gains or losses shall be apportioned to the line items affected by the hedged items. This apportionment shall be done on a systematic and rational basis and shall not result in the grossing up of the net gains or losses arising from a single hedging instrument.
4. An entity is not required to restate prior periods to reflect the application of these amendments. The entity may restate prior periods only if it is possible to do so without the use of hindsight. If an entity restates prior periods, the restated financial statements must reflect all the requirements in this Standard for the affected financial instruments. If an entity does not restate prior periods, the entity shall recognise any difference between the previous carrying amount and the carrying amount at the beginning of the annual reporting period that includes the date of initial application of these amendments in the opening retained earnings (or other component of equity, as appropriate) of the annual reporting period that includes the date of initial application of these amendments.
*International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS.
## Conclusions
Builders FirstSource Inc. Common Stock is assigned short-term Ba1 & long-term Ba1 estimated rating. Builders FirstSource Inc. Common Stock prediction model is evaluated with Ensemble Learning (ML) and Stepwise Regression1,2,3,4 and it is concluded that the BLDR stock is predictable in the short/long term. According to price forecasts for (n+6 month) period, the dominant strategy among neural network is: Sell
### BLDR Builders FirstSource Inc. Common Stock Financial Analysis*
Rating Short-Term Long-Term Senior
Outlook*Ba1Ba1
Income StatementCB3
Balance SheetBa3C
Leverage RatiosCaa2Caa2
Cash FlowCaa2Baa2
Rates of Return and ProfitabilityB1Baa2
*Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents.
How does neural network examine financial reports and understand financial state of the company?
### Prediction Confidence Score
Trust metric by Neural Network: 87 out of 100 with 857 signals.
## References
1. Efron B, Hastie T. 2016. Computer Age Statistical Inference, Vol. 5. Cambridge, UK: Cambridge Univ. Press
2. Athey S, Blei D, Donnelly R, Ruiz F. 2017b. Counterfactual inference for consumer choice across many prod- uct categories. AEA Pap. Proc. 108:64–67
3. R. Rockafellar and S. Uryasev. Conditional value-at-risk for general loss distributions. Journal of Banking and Finance, 26(7):1443 – 1471, 2002
4. Çetinkaya, A., Zhang, Y.Z., Hao, Y.M. and Ma, X.Y., Can neural networks predict stock market?(ATVI Stock Forecast). AC Investment Research Journal, 101(3).
5. Athey S, Imbens GW. 2017a. The econometrics of randomized experiments. In Handbook of Economic Field Experiments, Vol. 1, ed. E Duflo, A Banerjee, pp. 73–140. Amsterdam: Elsevier
6. Bera, A. M. L. Higgins (1997), "ARCH and bilinearity as competing models for nonlinear dependence," Journal of Business Economic Statistics, 15, 43–50.
7. V. Borkar. Q-learning for risk-sensitive control. Mathematics of Operations Research, 27:294–311, 2002.
Frequently Asked QuestionsQ: What is the prediction methodology for BLDR stock?
A: BLDR stock prediction methodology: We evaluate the prediction models Ensemble Learning (ML) and Stepwise Regression
Q: Is BLDR stock a buy or sell?
A: The dominant strategy among neural network is to Sell BLDR Stock.
Q: Is Builders FirstSource Inc. Common Stock stock a good investment?
A: The consensus rating for Builders FirstSource Inc. Common Stock is Sell and is assigned short-term Ba1 & long-term Ba1 estimated rating.
Q: What is the consensus rating of BLDR stock?
A: The consensus rating for BLDR is Sell.
Q: What is the prediction period for BLDR stock?
A: The prediction period for BLDR is (n+6 month)
|
2023-03-23 05:07:26
|
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https://risc.jku.at/publications/
|
## Publications
### On the Complexity of Unsatisfiable Primitive Recursively defined $\Sigma_1$-Sentences
#### David M. Cerna
In: T.B.D, , Proceedings of T.B.D, pp. 1-17. 2019. T.B.D. [pdf]
@inproceedings{RISC5841,
author = {David M. Cerna},
title = {{On the Complexity of Unsatisfiable Primitive Recursively defined $\Sigma_1$-Sentences}},
booktitle = {{T.B.D}},
language = {english},
abstract = {We introduce a measure of complexity based on formula occurrence within instance proofs of an inductive statement. Our measure is closely related to {\em Herbrand Sequent length}, but instead of capturing the number of necessary term instantiations, it captures the finite representational difficulty of a recursive sequence of proofs. We restrict ourselves to a class of unsatisfiable primitive recursively defined negation normal form first-order sentences, referred to as {\em abstract sentences}, which capture many problems of interest; for example, variants of the {\em infinitary pigeonhole principle}. This class of sentences has been particularly useful for inductive formal proof analysis and proof transformation. Together our complexity measure and abstract sentences allow use to capture a notion of {\em tractability} with respect to state-of-the-art approaches to inductive theorem proving, namely {\em loop discovery} and {\em tree grammar} based inductive theorem provers. We provide a complexity analysis of two important abstract sentences based on the infinitary pigeonhole principle which we conjecture represent the upper limits of tractability and the intractable with respect to the current approaches. },
pages = {1--17},
isbn_issn = {T.B.D},
year = {2019},
editor = {T.B.D},
refereed = {yes},
length = {17},
conferencename = {T.B.D}
}
### On the positivity of the Gillis–Reznick–Zeilberger rational function
#### V. Pillwein
Advances in Applied Mathematics 104, pp. 75 - 84. 2019. ISSN 0196-8858. [url]
@article{RISC5813,
author = {V. Pillwein},
title = {{On the positivity of the Gillis–Reznick–Zeilberger rational function}},
language = {english},
abstract = {In this note we provide further evidence for a conjecture of Gillis, Reznick, and Zeilberger on the positivity of the diagonal coefficients of a multivariate rational function. Kauers had proven this conjecture for up to 6 variables using computer algebra. We present a variation of his approach that allows us to prove positivity of the coefficients up to 17 variables using symbolic computation.},
journal = {Advances in Applied Mathematics},
volume = {104},
pages = {75 -- 84},
isbn_issn = { ISSN 0196-8858},
year = {2019},
refereed = {yes},
keywords = {Positivity, Cylindrical decomposition, Rational function, Symbolic summation},
length = {10},
url = {http://www.sciencedirect.com/science/article/pii/S0196885818301179}
}
### Automated Solution of First Order Factorizable Systems of Differential Equations in One Variable
#### J. Ablinger, J. Blümlein, P. Marquard, N. Rana, C. Schneider
Nucl. Phys. B 939, pp. 253-291. 2019. ISSN 0550-3213. arXiv:1810.12261 [hep-ph]. [url]
@article{RISC5795,
author = {J. Ablinger and J. Blümlein and P. Marquard and N. Rana and C. Schneider},
title = {{Automated Solution of First Order Factorizable Systems of Differential Equations in One Variable}},
language = {english},
journal = {Nucl. Phys. B},
volume = {939},
pages = {253--291},
isbn_issn = {ISSN 0550-3213},
year = {2019},
note = {arXiv:1810.12261 [hep-ph]},
refereed = {yes},
length = {39},
url = {https://www.sciencedirect.com/science/article/pii/S055032131830350X?via%3Dihub}
}
### A Family of Congruences for Rogers-Ramanujan Subpartitions
#### Nicolas Allen Smoot
Journal of Number Theory 196, pp. 35-60. March 2019. ISSN 0022-314X. [pdf]
@article{RISC5809,
author = {Nicolas Allen Smoot},
title = {{A Family of Congruences for Rogers--Ramanujan Subpartitions}},
language = {english},
abstract = {In 2015 Choi, Kim, and Lovejoy studied a weighted partition function, A1(m), which counted subpartitions with a structure related to the Rogers–Ramanujan identities. They conjectured the existence of an infinite class of congruences for A1(m), modulo powers of 5. We give an explicit form of this conjecture, and prove it for all powers of 5.},
journal = {Journal of Number Theory},
volume = {196},
pages = {35--60},
isbn_issn = {ISSN 0022-314X},
year = {2019},
month = {March},
refereed = {yes},
keywords = {Integer partitions, Partition congruences, Rogers--Ramanujan identities, Ramanujan--Kolberg identities, Modular functions},
sponsor = {FWF: W1214-N15},
length = {26}
}
### An Improved Method to Compute the Inverse Mellin Transform of Holonomic Sequences
#### J. Ablinger
In: Proceedings of "Loops and Legs in Quantum Field Theory - LL 2018, , PoS(LL2018) , pp. 1-10. 2018. ISSN 1824-8039. [url]
@inproceedings{RISC5789,
author = {J. Ablinger},
title = {{An Improved Method to Compute the Inverse Mellin Transform of Holonomic Sequences}},
booktitle = {{Proceedings of "Loops and Legs in Quantum Field Theory - LL 2018}},
language = {english},
series = {PoS(LL2018)},
pages = {1--10},
isbn_issn = {ISSN 1824-8039},
year = {2018},
editor = {J. Blümlein and P. Marquard},
refereed = {yes},
length = {10},
url = {https://pos.sissa.it/303/063/pdf}
}
### Anti-Unification and Natural Language Processing
#### N. Amiridze, T. Kutsia
In: Fifth Workshop on Natural Language and Computer Science, NLCS’18, , EasyChair preprints 203, pp. 1-12. 2018. [url] [pdf]
@inproceedings{RISC5707,
author = {N. Amiridze and T. Kutsia},
title = {{Anti-Unification and Natural Language Processing}},
booktitle = {{Fifth Workshop on Natural Language and Computer Science, NLCS’18}},
language = {english},
series = {EasyChair preprints},
number = {203},
pages = {1--12},
isbn_issn = { },
year = {2018},
editor = {A. Asudeh and V. de Paiva and L. Moss},
refereed = {yes},
length = {12},
url = {https://doi.org/10.29007/fkrh}
}
### Varieties of apolar subschemes of toric surfaces
#### Gallet Matteo, Ranestad Kristian, Villamizar Nelly
Ark. Mat. 56(1), pp. 73-99. 2018. ISSN 0004-2080. [url]
@article{RISC5796,
author = {Gallet Matteo and Ranestad Kristian and Villamizar Nelly},
title = {{Varieties of apolar subschemes of toric surfaces}},
language = {english},
journal = {Ark. Mat.},
volume = {56},
number = {1},
pages = {73--99},
isbn_issn = { ISSN 0004-2080},
year = {2018},
refereed = {yes},
length = {27},
url = {https://doi.org/10.4310/ARKIV.2018.v56.n1.a6}
}
### Varieties of apolar subschemes of toric surfaces
#### Gallet Matteo, Ranestad Kristian, Villamizar Nelly
Ark. Mat. 56(1), pp. 73-99. 2018. ISSN 0004-2080. [url]
@article{RISC5811,
author = {Gallet Matteo and Ranestad Kristian and Villamizar Nelly},
title = {{Varieties of apolar subschemes of toric surfaces}},
language = {english},
journal = {Ark. Mat.},
volume = {56},
number = {1},
pages = {73--99},
isbn_issn = { ISSN 0004-2080},
year = {2018},
refereed = {yes},
length = {27},
url = {https://doi.org/10.4310/ARKIV.2018.v56.n1.a6}
}
### Term-Graph Anti-Unification
#### Alexander Baumgartner, Temur Kutsia, Jordi Levy, Mateu Villaret
Technical report no. 18-02 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 2018. [pdf]
@techreport{RISC5549,
author = {Alexander Baumgartner and Temur Kutsia and Jordi Levy and Mateu Villaret},
title = {{Term-Graph Anti-Unification}},
language = {english},
number = {18-02},
year = {2018},
length = {19},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}
### Term-Graph Anti-Unification
#### Alexander Baumgartner, Temur Kutsia, Jordi Levy, Mateu Villaret
In: 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018), , Leibniz International Proceedings in Informatics (LIPIcs) 108, pp. 9:1-9:17. 2018. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, ISBN 978-3-95977-077-4 ISSN 1868-8969. [url]
@inproceedings{RISC5764,
author = {Alexander Baumgartner and Temur Kutsia and Jordi Levy and Mateu Villaret},
title = {{Term-Graph Anti-Unification}},
booktitle = {{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)}},
language = {english},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {108},
pages = {9:1--9:17},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
isbn_issn = {ISBN 978-3-95977-077-4 ISSN 1868-8969},
year = {2018},
editor = {Helene Kirchner},
refereed = {yes},
length = {17},
url = {http://drops.dagstuhl.de/opus/volltexte/2018/9179}
}
### On some polynomials and series of Bloch-Polya Type
#### Berkovich A., Uncu A. K.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 146(7), pp. 2827-2838. July 2018. 1088-6826. [url]
@article{RISC5557,
author = {Berkovich A. and Uncu A.~K.},
title = {{On some polynomials and series of Bloch-Polya Type}},
language = {english},
journal = {PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY},
volume = {146},
number = {7},
pages = {2827--2838},
isbn_issn = {1088-6826},
year = {2018},
month = {July},
refereed = {yes},
keywords = {Mathematics - Number Theory, Mathematics - Combinatorics, 05A17, 05A19, 11B65, 11P81},
length = {12},
url = {http://www.ams.org/journals/proc/2018-146-07/S0002-9939-2018-13982-9/}
}
### Some Elementary Partition Inequalities and Their Implications
#### Berkovich A., Uncu A. K.
ArXiv e-prints (to appear in Annals of Cobinatorics), pp. -. 2018. Preprint. [url]
@article{RISC5558,
author = {Berkovich A. and Uncu A.~K.},
title = {{Some Elementary Partition Inequalities and Their Implications}},
language = {english},
journal = {ArXiv e-prints (to appear in Annals of Cobinatorics)},
pages = {--},
isbn_issn = {Preprint},
year = {2018},
refereed = {yes},
keywords = {Mathematics - Combinatorics, Mathematics - Number Theory, 05A15, 05A17, 05A19, 05A20, 11B65, 11P81, 11P84, 33D15},
length = {12},
url = {https://arxiv.org/abs/1708.01957}
}
### Polynomial Identities Implying Capparelli's Partition Theorems
#### Ali Kemal Uncu, Alexander Berkovich
ArXiv e-prints (submitted), pp. -. 2018. N/A. [url]
@article{RISC5790,
author = {Ali Kemal Uncu and Alexander Berkovich},
title = {{Polynomial Identities Implying Capparelli's Partition Theorems }},
language = {english},
journal = {ArXiv e-prints (submitted)},
pages = {--},
isbn_issn = {N/A},
year = {2018},
refereed = {yes},
length = {21},
url = {https://arxiv.org/pdf/1807.10974.pdf}
}
### Elementary Polynomial Identities Involving q-Trinomial Coefficients
#### Ali Kemal Uncu, Alexander Berkovich
ArXiv e-prints (submitted), pp. -. 2018. N/A. [url]
@article{RISC5791,
author = {Ali Kemal Uncu and Alexander Berkovich},
title = {{Elementary Polynomial Identities Involving q-Trinomial Coefficients }},
language = {english},
journal = {ArXiv e-prints (submitted)},
pages = {--},
isbn_issn = {N/A},
year = {2018},
refereed = {yes},
length = {0},
url = {https://arxiv.org/abs/1810.06497}
}
### Refined q-Trinomial Coefficients and Two Infinite Hierarcies of q-Series Identities
#### Ali Kemal Uncu, Alexander Berkovich
ArXiv e-prints (submitted), pp. 1-10. 2018. N/A. [url]
@article{RISC5801,
author = {Ali Kemal Uncu and Alexander Berkovich},
title = {{Refined q-Trinomial Coefficients and Two Infinite Hierarcies of q-Series Identities }},
language = {english},
abstract = {We will prove an identity involving refined q-trinomial coefficients. We then extend this identity to two infinite families of doubly bounded polynomial identities using transformation properties of the refined q-trinomials in an iterative fashion in the spirit of Bailey chains. One of these two hierarcies contains an identity which is equivalent to Capparelli's first Partition Theorem. },
journal = {ArXiv e-prints (submitted)},
pages = {1--10},
isbn_issn = {N/A},
year = {2018},
refereed = {yes},
length = {10},
url = {https://arxiv.org/abs/1810.12048}
}
### Generalizing some Results in Field Theory for Rings
#### Jose Capco
Communications in Algebra, pp. 0-12. 2018. 0092-7872. Preprint. [pdf]
@article{RISC5375,
author = {Jose Capco},
title = {{Generalizing some Results in Field Theory for Rings}},
language = {english},
journal = {Communications in Algebra},
pages = {0--12},
isbn_issn = {0092-7872},
year = {2018},
note = {Preprint},
refereed = {no},
length = {13}
}
### Primitive Recursive Proof Systems for Arithmetic
#### David M. Cerna
RISC. Technical report, January 2018. In revision. [pdf]
@techreport{RISC5528,
author = {David M. Cerna},
title = {{Primitive Recursive Proof Systems for Arithmetic}},
language = {english},
abstract = {Peano arithmetic, as formalized by Gentzen, can be presented as an axiom extensionof the LK-calculus with equality and an additional inference rule formalizing induction.While this formalism was enough (with the addition of some meta-theoretic argumentation)to show the consistency of arithmetic, alternative formulations of induction such asthe infinitary ω-rule and cyclic reasoning provide insight into the structure of arithmeticproofs obfuscated by the inference rule formulation of induction. For example, questionsconcerning the elimination of cut, consistency, and proof shape are given more clarity. Thesame could be said for functional interpretations of arithmetic such as system T whichenumerates the recursive functions provably total by arithmetic. A key feature of thesevariations on the formalization of arithmetic is that they get somewhat closer to formalizingthe concept of induction directly using the inferences of the LK-calculus, albeit byadding extra machinery at the meta-level. In this work we present a recursive sequentcalculus for arithmetic which can be syntactically translated into Gentzen formalism ofarithmetic and allows proof normalization to the LK-calculus with equality.},
year = {2018},
month = {January },
note = {In revision},
institution = {RISC},
length = {20}
}
### Idempotent Anti-unification
#### David M. Cerna Temur Kutsia
RISC. Technical report, Feb. 2018. Submitted for review. [pdf]
@techreport{RISC5530,
author = {David M. Cerna Temur Kutsia},
title = {{Idempotent Anti-unification }},
language = {english},
abstract = {In this paper we address two problems related to idempotent anti-unification. First, we show thatthere exists an anti-unification problem with a single idempotent symbol which has an infiniteminimal complete set of generalizations. It means that anti-unification with a single idempotentsymbol has infinitary or nullary generalization type, similar to anti-unification with two idem-potent symbols, shown earlier by Loı̈c Pottier. Next, we develop an algorithm, which takes anarbitrary idempotent anti-unification problem and computes a representation of its solution set inthe form of a regular tree grammar. The algorithm does not depend on the number of idempotentfunction symbols in the input terms. The language generated by the grammar is the minimalcomplete set of generalizations of the given anti-unification problem, which implies that idem-potent anti-unification is infinitary.},
year = {2018},
month = {Feb.},
note = {Submitted for review},
institution = {RISC},
length = {27}
}
### A General Recursive Construction for Schematic Resolution Derivations
#### David M. Cerna
2018. submitted for review. Preprint. [pdf]
@techreport{RISC5594,
author = {David M. Cerna},
title = {{A General Recursive Construction for Schematic Resolution Derivations}},
language = {english},
abstract = {Proof schemata provide an alternative formalism for handling inductive argumentation, while non-trivially extending {\em Herbrand's theorem} to a fragment of arithmetic and thus allowing the construction of {\em Herbrand sequents} and {\em expansion trees}. Existing proof analysis methods for proof schemata extract an unsatisfiable characteristic formula representing the cut structure of the proof and from its refutation construct a Herbrand sequent. Unfortunately, constructing the refutation is a task which is highly non-trivial. An automated method for constructing such refutations exists, but it only works for a very weak fragment of arithmetic and is hard to use interactively. More expressive yet interactive methods for the formalization of recursive resolution refutation are complex, hard to work with, and still limited to an undesirably weak class of recursion. In this work we note a particular problem with previous methods, namely they mix the recursive structure with the calculus of refutation. Also we present a modular recursive structure independent of the resolution formalism and proof construction. We illustrate the expressive power of the so called {\em finite saturated tree} formalism by formalizing the Non-injectivity Assertion's schematic refutation (a variant of the infinitary Pigeonhole principle). None of the previously developed formalism are able to formalize this refutation.},
year = {2018},
note = {submitted for review},
length = {42},
type = {Preprint},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}
### Higher-Order Equational Pattern Anti-Unification
#### David M. Cerna, Temur Kutsia
In: 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018), , Leibniz International Proceedings in Informatics (LIPIcs) 108, pp. 12:1-12:17. 2018. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, ISBN 978-3-95977-077-4 ISSN 1868-8969. [url]
@inproceedings{RISC5765,
author = {David M. Cerna and Temur Kutsia},
title = {{Higher-Order Equational Pattern Anti-Unification}},
booktitle = {{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)}},
language = {english},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {108},
pages = {12:1--12:17},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
isbn_issn = {ISBN 978-3-95977-077-4 ISSN 1868-8969},
year = {2018},
editor = {Helene Kirchner},
refereed = {yes},
length = {17},
url = {http://drops.dagstuhl.de/opus/volltexte/2018/9182}
}
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2019-01-17 03:10:53
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http://www.best-wines.eu/link/11882/magnetic-field-of-a-cylinder.html
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## E-mail:[email protected]
### Timings : 24 hours all day
• Home
• magnetic field of a cylinder
# magnetic field of a cylinder
• ### Lecture Notes Chapter 1 - University of Rochester
The magnetic field outside an infinitely long solenoid is ... The field inside a needle-shaped cylinder of magnetization is approximately equal to the field inside an ...
• ### Chapter 28 Magnetic Fields Sources - Experimental …
Chapter 28 –Magnetic Fields Sources All known magnetic sources are due to magnetic dipoles and inherently ... • A cylinder of radius R carrying a current I.
• ### Magnetic Field Cylinders - American Cylinder
Magnetic Field Cylinders. Easily Configure and Download Cad Files Display This Product Catalog Order Cylinders and Accessories Online STANDARD FEATURES AND BENEFITS. 1 Cylinder Body. Stainless Steel: Type 304 Stainless Steel manufactured to special mill specifications and tolerances to insure a long cylinder life. Aluminum 76 …
• ### A cylinder on an inclined plane — Collection of Solved ...
A cylinder on an inclined plane ... The cylinder is situated in a magnetic field of an induction B = 0.5 T. The magnetic field is oriented vertically as shown in the ...
• ### 2.7.11 Magnetic field of cylinder domains. NT-MDT …
2.7.11 Magnetic field of cylinder domains. NT-MDT Spectrum Instrument - Your AFM & Raman AFM - TERS company
• ### Physics for Science & Engineering II | Example: Magnetic ...
from Office of Academic Technologies on Vimeo. Example- Magnetic field of a coaxial cable. Now let’s calculate the magnetic fields of a coaxial cable in different ...
• ### Magnetic field of a wire within a hollow cylinder ...
Nov 03, 2013· Oh, my upper bound goes to little r. So that changes my value of B(inside wire) = (mu-knot) * I / 4(pi) *R(wire) For next question, magnetic field in space between cylinder and wire I believe would be the same as part a.
• ### Eðlisfræði 2, vor 2007 - University of Iceland
Eðlisfræði 2, vor 2007 29b. ... Think of the magnetic field outside the cylinder as an applied field plus a magnetic field due to the cylinder.
• ### Magnetic field inside and outside cylinder with varying ...
I am reading through Introduction to Electrodynamics by David J. Griffiths and came across the following problem:. A steady current $I$ flows down a long cylindrical wire of radius $a$. Find the magnetic field, both inside and outside the wire if the current is distributed in such a way that $J$ is proportional to $s$, the distance from the axis.
• ### Wolfram Demonstrations Project
Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.
• ### Biot-Savart's Law & Ampere's Law | MIT OpenCourseWare ...
Biot-Savart's Law & Ampere's Law Exam Prep ... Magnetic Field of a Spinning Cylinder. Find the magnetic field of a standard solenoid and compare it to the ...
• ### Example A Hollow Tube of Current - KU ITTC
11/21/2004 Example A Hollow Tube of Current 1/7 ... the magnetic flux density outside the current cylinder is ... Note the field outside of the cylinder (ρ>c) ...
• ### CHAPTER MAGNETIC FIELD IN MATERIALS
CHAPTER 13: MAGNETIC FIELD IN MATERIALS 117 is parallel to the cylinder axis, or (2) M is perpendicular to the axis? - (a) In case 1, surface currents on the two ...
• ### 60. Physics | Magnetic Effects | Magnetic Energy Inside …
Jul 07, 2014· Physics | Magnetic Effects | Magnetic Energy Inside a Long ... Magnetic Field from Moving ... Using Ampere's Law to Find the Field of a Metallic Cylinder ...
• ### Halbach array - Wikipedia
A Halbach array is a special arrangement of permanent magnets that augments the magnetic field on one side of the array while cancelling the field to near zero on the other side. This ...
A solid cylinder carries a current density J along ... find the magnitude of the magnetic field B in ... Calculate the displacement current-density jD between ...
• ### The Field near an Infinite Cylinder
The Field near an Infinite Cylinder. Remember when we were looking at electric fields inside and outside charged spherical shells? We used Gauss' Law to show that the field inside the shell was zero, and outside the shell the electric field was the same as the field from a point charge with a charge equal to the charge on the shell and placed at …
• ### 9.3 - Massachusetts Institute of Technology
Magnetic Field Intensity of a Uniformly Magnetized Cylinder. The cylinder shown in Fig. 9.3.1 is uniformly magnetized in the z direction, M = M o i z. The first step toward finding the resulting H within the cylinder and in the surrounding free space is an evaluation of the distribution of magnetic charge density. The uniform M has no ...
• ### Spinning Cylinder Experiments - resonantfractals.org
Spinning Cylinder Experiments. ... Feeling the Proton layer of the copper atom, and connecting this with a magnetic field in real life, rather then merely in theory.
• ### Magnetic field of steady currents - Britannica.com
Magnetic field of steady currents. Magnetic fields produced by electric currents can be ... wire tightly around a long hollow cylinder. The value of the field is.
• ### 8.4 - Massachusetts Institute of Technology
Figure 8.4.1 Perfectly conducting circular cylinder of radius R in a magnetic field that is y directed and of magnitude H o far from the cylinder.
• ### K&J Magnetics - Magnetic Field Calculator
The K&J Magnetic Field Calculator calculates the magnetic field strength in Gauss near a disc or cylinder shaped neodymium magnet. Enter the size of …
• ### homework and exercises - Magnetic field inside of a …
I have a simple question. I need to find out what is the magnetic field inside a rotating long cylinder with a charged density $\sigma$. The cylinder rotates around its axis with angular speed \$\o...
• ### Gaussian surface - Wikipedia
A Gaussian surface (sometimes ... or magnetic field. ... disks at the ends of the field at a perpendicular angle and the side of the cylinder are parallel to the ...
• ### : Magnetic Cylinder
Search results. 1-16 of over 2,000 results for "Magnetic Cylinder" "Magnetic Cylinder"
• ### An analytical computation of magnetic field generated …
An analytical formulation to compute a magnetic field generated from an uniformly magnetized cylinder ferromagnet is developed. Exact solutions of the magnetic field ...
• ### Calculate magnetic flux density with formula - …
How do you calculate the magnetic flux density? The magnetic flux density is also called "B field" or "magnetic ... of the field of a larger cylinder magnet ...
• ### The Magnetic Field of a Hollow Wire - photonics101
The magnetic field of a hollow wire is calculated. Electrodynamics . Electrostatics ... A Cylinder Shell Current and its Magnetic Field; Providing a Homogeneous Magnetic Field - The Helmholtz Coil ; Search ... ...
• ### Magnetic Field from a Cylinder’s Magnetization | David …
It is not intuitively obvious how an object’s magnetization relates to the magnetic field it generates. To develop a better physical picture of this phenomena ...
• ### The Magnetic Field of the "Cylinder Shell Current ...
The magnetic field for a current distribution in form of a cylinder shell is determined.
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2019-03-22 06:51:06
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http://tex.stackexchange.com/questions/89828/appendix-package-option-to-force-page-break-before-appendices
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# Appendix package option to force page break before appendices
Instead of manually putting a \newpage before \begin{appendices}, how can I tell the appendix package to do this ?
-
If you have a chaptered document class, this would be the default behaviour. In documents with top level structure section there is no way to tell the appendix package to insert a page break. That is because sections usually do not start new pages. So you need to manually add a \clearpage.
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2016-02-08 04:32:36
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https://mathematica.stackexchange.com/questions/156203/replace-variable-in-series-expression
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# Replace variable in Series expression
I am trying to generate a series expansion in terms of the variable t then substitute a value in for it. However it seems that something about the SeriesData object returned by Series doesn't permit a standard slashdot replacement.
Series[(a^4 - (a - t)^4), {t, 0, 4}] // Normal /. t -> a/20
returns
4 a^3 t - 6 a^2 t^2 + 4 a t^3 - t^4
which is the same result as though the slashdot isn't even there.
On the other hand, replacing prior to Normal results in an undesirable output.
Series[a^4 - (a - t)^4 , {t, 0, i}] /. t -> a/20 // Normal
returns
(4 a^3 a)/20 - 6 a^2 (a/20)^2 + 4 a (a/20)^3 - (a/20)^4 + O[a/20]^6
This is on the right track, but I am left with the BigO and no amount of Simplify or its related functions can get the expression to condense to C*a^4.
To further complicate things, I am trying to run this within a For loop where I increment the number of kept terms.
For[i = 1, i <= 4, i++,
Print[Series[a^4 - (a - t)^4), {t, 0, i}] // Normal /. t -> a/20]]
So, how can I do the Series expansion, substitute a/20 in for t, and get a nice output that is, ideally, some constant times a^4. Much thanks.
• Normal@Series[(a^4 - (a - t)^4), {t, 0, 4}] /. t -> a/20. Operator precedence. in other words, implicitly, your original expression is interpreted like this: Series[(a^4 - (a - t)^4), {t, 0, 4}] // (Normal /. t -> a/20). – march Sep 20 '17 at 22:00
• That's a notation with which I am unfamiliar. But thank you. – saintsfan342000 Sep 20 '17 at 22:05
(As march beat me to comment) I think you have a precedence problem with the postfix application //. Try this:
(Series[(a^4 - (a - t)^4), {t, 0, 4}] // Normal) /. t -> a/20
(29679 a^4)/160000
• If /. had a lower binding power then things like {1, 2, 3} /. {2 -> 7} // Print would group like {1, 2, 3} /. ({2 -> 7} // Print) which is totally undesirable in most cases in my experience. // is specifically useful because of its low binding power allowing most things on the left-hand-side to "stay together." That the right hand side, e.g. // Normal /. t -> a/20 is also grouped together is merely an unfortunate consequence, though this too can at least occasionally be exploited usefully. – Mr.Wizard Sep 21 '17 at 6:39
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2020-01-17 20:09:19
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http://clay6.com/qa/26458/a-red-solid-is-insoluble-in-water-however-it-becomes-soluble-if-some-ki-is-
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Browse Questions
# A red solid is insoluble in water. However, it becomes soluble if some KI is added to water. Heating red solid in a test tube produces violet coloured fumes and droplets of metal appear on the cooler parts of test tube. The red solid is
(a) $(NH_4)_2Cr_2O_7$
(b) $HgI_2$
(c) $HgO$
(d) $Pb_3O_4$
Answer: $HgI_2$
$HgI_2$ is a scarlet red compound which is insoluble in water
$HgI_2 + 2KI \longrightarrow K_2(HgI_4)$ (soluble)
$HgI_2 \xrightarrow{\Delta} Hg + I_2$ (violet vapour droplet)
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2016-12-02 19:48:52
|
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https://maths.mt/walks/
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Walks and CDCs
A lot of the mathematical research I have been conducting recently, primarily in collaboration with my undergraduate supervisor Prof. Irene Sciriha, has been related to walks, CDCs and TF-isomorphisms.
This webpage provides the basic definitions necessary for understanding what I've been working on, together with various resources, most notably a Wolfram Mathematica™ package for graph computations.
Basic Definitions
The walk matrix of a graph is the matrix with columns $\mathbf W = \begin{pmatrix}| & | & | & & | \\ \boldsymbol j & \mathbf A\boldsymbol j & \mathbf A^2\boldsymbol j & \cdots & \mathbf A^{p-1}\boldsymbol j \\ | & | & | & & | \end{pmatrix},$ where $$\mathbf A$$ is the adjacency matrix of the graph, $$\boldsymbol j$$ is the all-ones vector $$(1,\dots,1)$$ and $$p$$ is the largest positive integer for which the columns of $$\mathbf W$$ remain linearly independent. It is not difficult to see that the $$ij$$th entry in the matrix is the number of distinct walks of length $$j$$ in the graph starting from vertex $$i$$.
The canonical double cover of a graph $$G$$ is the graph obtained by making two copies of the vertex set of $$G$$, and connecting the vertices in one copy to the neighbours it originally had in the other; here are two examples.
The question we studied was mainly the following: what can we say about two graphs $$G$$ and $$H$$ if $$\operatorname{CDC}(G)\simeq\operatorname{CDC}(H)$$? For instance, if $$G$$ is connected, it's not necessarily the case that $$H$$ is connected: $\operatorname{CDC}(2\,K_3) \simeq 2\,C_6 \simeq \operatorname{CDC}(C_6).$ On the other hand, if $$G$$ has an isolated vertex, $$H$$ must have one. This gave rise to a nice, rather powerful proof technique: in order to prove a statement $$\varphi$$, we assume that $$G$$ has no isolated vertices, and that $$\operatorname{CDC}(G)=\operatorname{CDC}(H)$$. Then we show $$\lnot\varphi$$ implies that $$H$$ has an isolated vertex, which is a contradiction.
Using this technique, we were able to show that "$$G$$ and $$H$$ have the same CDC'' is equivalent to a weaker version of isomorphism (which Lauri et. al. called a two-fold isomorphism): that there are two permutation matrices $$\mathbf P$$ and $$\mathbf Q$$ such that the adjacency matrices satisfy $$\mathbf P\mathbf A_G\mathbf Q = \mathbf A_H$$. (Ordinary graph isomorphisms correspond to a single permutation matrix $$\mathbf P$$ such that $$\mathbf P\mathbf A_G\mathbf P^{-1} = \mathbf A_H$$.) But this does not add much freedom to generate such graph pairs, since given two random permutation matrices, it is highly unlikely that $$\mathbf P\mathbf A_G\mathbf Q$$ is also the adjacency matrix of some other graph. Indeed, on $$n\leq 8$$ vertices, for any two graphs $$G$$ and $$H$$, I found that $\mathrm P(\text{$$G$$ and $$H$$ are isomorphic} \mid \text{they have the same CDC}) = 0.99999965,$ since of all the possible $$\binom{13\,597}2$$ pairs of non-isomorphic graphs on $$n\leq 8$$ vertices, there are only 32 which have the same CDC. It turns out (and we showed that) having the same CDC implies that the walk matrices are the same; which means that the graphs same number of walks of any length, once an appropriate correspondence of the vertices is established. This is the essential "shared structure" which having the same CDC implies, and it partly explains why it is so rare for a pair of graphs to have the same CDC yet not be isomorphic.
In my undergraduate dissertation, I went on to establish a hierarchy of relationships which pairs of graphs can have, involving CDC's, and the standard spectral objects which appear in the theory of walks in graphs (walk matrices, main eigenvalues, main eigenspaces, etc.). While conducting research to establish some of these, a lot of visually appealing examples of graph pairs cropped up, some of them are shown above. This hierarchy was published recently in the journal Discussiones Mathematicæ Graph Theory, and in the same paper there is also a list of all 32 non-isomorphic graph pairs with isomorphic CDCs. This list is available in PDF form in the appendix of my undergraduate dissertation, or in the section below.
Graphs with the same CDC
While I was working on my undergraduate dissertation, I obtained an exhaustive list of all pairs of non-isomorphic graphs on ≤ 8 vertices which have the same CDC (i.e., all the pairs of graphs which are TF-isomorphic). I've recently also computed all such pairs on 9 vertices. You can download the corresponding graph numbers in CSV format below.
The numbers correspond to the graphs in Brendan McKay's graph data. You can easily import these graphs into Mathematica, e.g.,
Notice I've made use of some commands from the Walks package which you can obtain below.
Graphs with the same CDC on 8 Vertices
I've made the detailed list of pairs on 8 vertices available on this webpage. In addition to the pairs, you can find their walk matrices, eigenvalues, CDCs and animated Ryser switches.
Mathematica Package
Wolfram Mathematica™ is an incredibly powerful piece of software which can perform almost any kind of computation imaginable, and unsurprisingly it is very handy for performing computations on graphs. (Unfortunately Mathematica is not free, neither in the libre sense, nor in the gratis sense, but if you are a student you can probably get it for free.)
The Walks Mathematica package, in addition to various walk/CDC related commands, provides plenty of nice commands which are useful for working with matrices of graphs in general. It is very easy to download and install.
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2021-11-29 03:38:09
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https://redoste.xyz/2020/04/21/modding-wii-sports-part-i-identifying-files-and-creating-a-debug-output/
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## Modding Wii Sports : Part I : Identifying files and creating a debug output
2020-04-21 16:00 +0200
A few months ago I saw someone playing Wii Sports doing some Golf. This reminded me I always wanted to create custom golf tracks. After a little bit of search, I found out that nobody really did it. Some people were asking if someone did it and they were a few attempts on Wii Sport Resort (here, here or here) but I found no real public source code or walkthrough of how to do your own custom golf track on the original Wii Sports.
After struggling for multiples weeks now I will show you my current (slow) progress and I hope I will be able to continue this series of blog posts up until a complete usable mod. The best would be an easy to use tool that allow a conversion of any 3D models into a golf course and a user interface on the Wii that allow loading custom tracks from the SD card. For the moment I’m not skilled enough nor I have enough time but maybe writing blog posts will encourage me to continue…
# I - Identifying existing files
The first easy step was to rip the original disc. I own an original Wii Sports European disc, it is the second revision that have some bug patched. I used USBLoaderGX, it’s a backup loader that allow to copy discs to an USB drive. It produces a WBFS file, it is a custom file format that only contain useful part of the ISO, by removing all the padding an image can shrink from 4GiB to a few hundreds of MiB (it, of course, depends of the game).
To extract and rebuild WBFS images I used the Wiimms ISO Tools suite.
$# We can easily extract the content of the original image$ wit X RSPP01.wbfs RSPP01/
***** wit: Wiimms ISO Tool v3.02a r0 x86_64 - Dirk Clemens - 2020-03-07 *****
wit: EXTRACT 1/1 WBFS:RSPP01.wbfs/#0 -> RSPP01/
$# And rebuild the modded one after some work$ wit CP RSPP01.modded/ RSPP01.modded.wbfs
***** wit: Wiimms ISO Tool v3.02a r0 x86_64 - Dirk Clemens - 2020-03-07 *****
* COPY/SCRUB 1/1 FST:RSPP01.modded/ -> WBFS:RSPP01.modded.wbfs
After a little bit of search, we can identify two important things:
• The sys/main.dol file, it is the main game binary in the DOL format (the executable format for the Wii and the GameCube)
• The files/Stage/RPGolScene/ folder, it contains a file per golf track. The name of most of the file is in the form glf_course_fcX.carc where fc is for Family Computer or Famicom (the Japanese version of the NES) and the number identify the number of the track it corresponds to in the 1984 Golf NES game.
total 17M
1,8M glf_course_E3.carc
258K glf_course_angle.carc
1,6M glf_course_fc1.carc
1,3M glf_course_fc11.carc
1,1M glf_course_fc12.carc
1,8M glf_course_fc13.carc
1,3M glf_course_fc14.carc
1,8M glf_course_fc16.carc
367K glf_course_fc18.carc
1,1M glf_course_fc3.carc
1,6M glf_course_fc5.carc
1,9M glf_course_fc8.carc
1,3M glf_course_fc9.carc
212K glf_course_survey.carc
These carc files are in fact Yaz0 compressed U8 archives. Another Wiimms tool suite can be used to extract these files: the Wiimms SZS Toolset.
Here is the content of glf_course_fc1.carc:
$wszst LL glf_course_fc1.carc * Files of YAZ0.U8:glf_course_fc1.carc size/dec magic file or directory ------------------------------------------------------------------------------- 687202 ...< glf_course_fc1.kcl 10600 PMPF glf_course_fc1.pmp - - G3D/ 999424 bres G3D/glf_course_fc1.brres 179712 bres G3D/glf_map_fc1.brres - - glf_scene_fc1/ 164 PBLM glf_scene_fc1/glf_scene_fc1.pblm 1352 LGHT glf_scene_fc1/glf_scene_fc1.plight 408 LMAP glf_scene_fc1/glf_scene_fc1.plmap ## 1 - The glf_course_fc1.kcl file The kcl file format is the same used in the Mario Kart Wii game to describe the collision of a the track. We can suppose this one also describe the collision of the golf track. Using wkclt from the Wiimms SZS Toolset, we can convert the kcl into a simple Wavefront obj file $ wkclt DEC glf_course_fc1.kcl
DECODE KCL:glf_course_fc1.kcl -> KCLTXT:./glf_course_fc1.obj
* CHECK KCL:glf_course_fc1.kcl
- HINT: 1 of 8398 drivable triangles is face down => --kcl=RM-FACEDOWN
- HINT: 1 of 8398 drivable triangles is face down (>30°).
=> No warnings and 2 hints for KCL:glf_course_fc1.kcl
$ll glf_course_fc1.* -rw-r--r-- 1 redoste redoste 672K 1970-01-01 00:00 glf_course_fc1.kcl -rw-r--r-- 1 redoste redoste 19K 1970-01-01 00:00 glf_course_fc1.mtl -rw-r--r-- 1 redoste redoste 911K 1970-01-01 00:00 glf_course_fc1.obj And of course the opposite is possible $ wkclt ENC glf_course_fc1.obj
ENCODE KCLTXT:glf_course_fc1.obj -> KCL:./glf_course_fc1.kcl
* CHECK KCLTXT:glf_course_fc1.obj
- HINT: 1 of 8398 drivable triangles is face down => --kcl=RM-FACEDOWN
- HINT: 1 of 8398 drivable triangles is face down (>30°).
=> No warnings and 2 hints for KCLTXT:glf_course_fc1.obj
- create octree: rshift=10, n_bcube=256, cube_size=512..1048576, blow=400, max_tri=30, max_depth=10, fast=0
Here is what glf_course_fc1.obj looks like imported into Blender :
Since wkclt have been thought for Mario Kart Wii the objects are not correctly named but they correspond to the different kind of ground available in the game (Green, Bunker, etc.) :
## 2 - The G3D/*.brres files
The brres files are some sort of archives that describe a 3D model. This archive is split in sections each one represents a specific part of the object (Model, Texture, Animations…). Since brres files are common to Mario Kart Wii and Super Smash Bros. Brawl, we can use the BrawlBox tool.
BrawlBox is a huge Windows tool that allow easy manipulation of brres archives and its different sections. Because I use GNU/Linux I had to do a little bit of tinkering to run BrawlBox with Wine. Installing dotnet48 using winetricks seems to do the job.
Here is what G3D/glf_course_fc1.brres looks like in BrawlBox :
The other brres file: G3D/glf_map_fc1.brres corresponds to the minimap visible in game in the bottom left corner. The map in it self is at the exact same scale as the original, it is only scaled down at the final rendering, making the creation of the map from the original course really easy.
Here is what G3D/glf_map_fc1.brres looks like in BrawlBox :
## 3 - The glf_scene_fc1/*.p* files
These three files seem to be used to polish the rendering of the map, but I was able to identify only one of them. The plight file seems to match the BLIGHT format since its magic number is the same (LGHT). However leaving the folder empty seems to do the trick since the map loads without any problem.
## 4 - The glf_course_fc1.pmp file
I was unable to clearly identify the format of the pmp file but I think it contains things such as the starting point, the ending point of the course and the position of trees. Its format should be similar to the KMP format of Mario Kart Wii since it is its purpose.
## 5 - Demo
The first easy demo I can do is making the map flat. For this I converted the KCL file to an OBJ file and set the Y value of every vertices to 0.
Then I used the scripting feature of BrawlBox to export every objects vertices from the model. The script is based on the builtin one made to export textures.
# Script to export or import objects vertices from brres files
from BrawlBox.API import bboxapi
from BrawlLib.SSBB.ResourceNodes import *
def search(node):
if isinstance(node, MDL0VertexNode):
return [node]
list = []
for child in node.Children:
list += search(child)
return list
if bboxapi.RootNode != None:
root = bboxapi.RootNode
for item in search(root):
print item.Name
# Use Replace to import and Export to export
item.Export("C:\\inp\\vec\\" + item.Name + ".vec")
#item.Replace("C:\\inp\\vec\\" + item.Name + ".vec")
print("Done!")
else:
bboxapi.ShowMessage('Cannot find Root Node (is a file open?)','Error')
Then I made a (extremely ugly and unreadable) Python script to flatten the object before reimporting them to the brres.
import struct
import sys
wo_offset = 0
def wo(b):
global wo_offset
wo_offset += len(b)
sys.stderr.buffer.write(b)
inf = open(sys.argv[1], "rb")
min_x, min_y, min_z = struct.unpack(">fff", inf.read(12))
max_x, max_y, max_z = struct.unpack(">fff", inf.read(12))
# Check and write the header
wo(struct.pack(">I", file_length))
wo(struct.pack(">I", mdl0_offset))
wo(struct.pack(">I", data_offset))
wo(struct.pack(">I", name_offset))
wo(struct.pack(">I", index))
if comp_count != 0x1:
print("comp_count != 1")
sys.exit(1)
wo(struct.pack(">I", comp_count))
if vec_format != 0x4:
print("vec_format != 4")
sys.exit(1)
wo(struct.pack(">I", vec_format))
if divisor != 0:
print("divisor != 0")
sys.exit(1)
wo(struct.pack(">B", divisor))
if stride != 0xc:
print("stride != 0xc")
sys.exit(1)
wo(struct.pack(">B", stride))
print("n_vec = {}".format(n_vec))
wo(struct.pack(">H", n_vec))
print("min = {},{},{}".format(min_x, min_y, min_z))
print("max = {},{},{}".format(max_x, max_y, max_z))
min_y = 0
max_y = 0
print("min = {},{},{}".format(min_x, min_y, min_z))
print("max = {},{},{}".format(max_x, max_y, max_z))
wo(struct.pack(">fff", min_x, min_y, min_z))
wo(struct.pack(">fff", max_x, max_y, max_z))
for _ in range(8):
wo(b"\x00")
inf.seek(data_offset)
for n in range(n_vec):
x, y, z = struct.unpack(">fff", inf.read(12))
print("n = {} : {},{},{}".format(n, x, y, z))
y = 0
wo(struct.pack(">fff", x, y, z))
for _ in range(file_length - wo_offset):
wo(b"\x00")
sys.stderr.buffer.flush()
After packing everything back up, we can rebuild the game image and admire this amazing flat golf course with flying trees, starting point and ending point !
# II - Reverse-engineering the binary
The main game binary is in the DOL format, it’s a pretty simple format and was able to open it in Ghidra pretty easily. I’m far from being skilled enough to completely reverse-engineer the binary but using simple string searches and X-refs I was able to identify important functions : reading files, reading archives, loading maps and I think I even identified the one responsible of parsing the unknown pmp file.
Here is the list of function identified (for the second European version I own : sha1sum main.dol : 0328a87d999995f95592f91c8d948d9995bb06bd)
• crash : 0x8010ab58
• get_lang_code : 0x80186410
• golf_get_fc_string : 0x8029db44
• golf_load_kcl_pmp : 0x80293d5c
• golf_load_stage_common_carc : 0x8028eb84
• golf_process_kcl? : 0x802a7414
• golf_process_pmp? : 0x801bf824
• golf_process_pmp?2 : 0x801bf890
• heap_alloc : 0x800a2e38
• heap_alloc_wraper : 0x800a3250
• load_from_carc : 0x80187a44
• load_from_carc_in_filelist : 0x8028eb68
• load_locales : 0x801877d0
• print_serial : 0x801840dc
• sprintf : 0x802aaf00
• strcat : 0x800b8e40
What made the process really hard and sometimes impossible for me is that I don’t know a lot PowerPC assembly so I generally blindly trusted Ghidra decompiler and only looked at the manual when required but most importantly this is C++ code, so we have to deal with all the C++ annoying stuff. To make this thing even more hard, Nintendo should use some weird custom compiler because it uses r13 to store the this pointer instead of using the first function argument like any other compilers but most importantly r13 point to the end of the structure ! Ghidra doesn’t seem to support looking at structure from the end and having to subtract offsets from the pointer so it just decompiles it to unreadable garbage pointer arithmetic.
Here is my favorite one (from golf_get_fc_string) :
return (&PTR_s_fc1_803e1fe0)[*(int *)(*(int *)((int)local_r13_-1 + -0x5abc) + 0x98) * 9];
Edit : 2020-04-22 23:20 +0200 : u/Leseratte10 mentioned on reddit that r13 is used for the Small Data Area. Because PowerPC is a RISC architecture there is a really small number of instructions, something as simple as accessing a global variable can take 2 instructions. To compensate, the compiler put all frequently accessed globals in this Small Data Area (here it is 64KiB large) and makes r13 constant by initialising it in the entry point function. Now globals in the Small Data Area can be accessed with only one instruction.
This problem was already discussed in a Ghidra Github issue. After installing a custom language definition for the Gekko and Broadway CPUs and reanalysing the whole binary, the r13 register is now considered constant. Using the Register Manager of Ghidra, we can set the value of r13 (here it is 0x804df900) and now decompilation makes way more sense.
Here is the previous snippet of golf_get_fc_string correctly decompiled :
return (&PTR_DAT_803e1fe0)[*(int *)(DAT_804d9e44 + 0x98) * 9];
The this pointer is correctly passed as the first argument of functions (via r3).
To finish this part on a positive note, some of the code is shared with Mario Kart Wii (yes, again) so here is this amazing decompilation project of Mario Kart Wii by riidefi that helped me a lot : https://github.com/riidefi/MKWDecompilation
# III - Adding a custom debug output
While working on custom maps, the game crashed, a lot. So to understand why it crashed I generally enabled the Dolphin debugger and followed the backtrace, looking at what functions it corresponds in Ghidra. A lot of this crashes where due to failed asserts and the asserts called print_serial before calling crash. This print_serial just seems to backup some registers to locals before returning. I think they removed the debug output in the final release.
print_serial
stwu r1,local_70(r1)
bne cr1,LAB_80184104
stfd f1,local_48(r1)
stfd f2,local_40(r1)
stfd f3,local_38(r1)
stfd f4,local_30(r1)
stfd f5,local_28(r1)
stfd f6,local_20(r1)
stfd f7,local_18(r1)
stfd f8,local_10(r1)
LAB_80184104
stw r3,local_68(r1)
stw r4,local_64(r1)
stw r5,local_60(r1)
stw r6,local_5c(r1)
stw r7,local_58(r1)
stw r8,local_54(r1)
stw r9,local_50(r1)
stw r10,local_4c(r1)
blr
To get this debug output working I didn’t want to patch the binary since I don’t know how to easily output the strings so I just modified the code of the emulator instead !
Since Dolphin is open source, it was really easy. I edited the code of the branch instruction to print strings when the destination address is the one of print_serial. Because print_serial should behave like printf and that the memory of the emulated console is only available via functions emulating the memory bus, the easiest thing to do was to create a simple and incomplete printf implementation.
// In Source/Core/Core/PowerPC/Interpreter/Interpreter_Branch.cpp
void Interpreter::bx(UGeckoInstruction inst)
{
if (inst.LK)
LR = PC + 4;
if (inst.AA)
NPC = SignExt26(inst.LI << 2);
else
NPC = PC + SignExt26(inst.LI << 2);
// Here is my incomplete ugly printf implementation
if (NPC == 0x801840dc) {
uint32_t gpr3 = PowerPC::ppcState.gpr[3];
int r = 4;
char c, t;
do {
gpr3++;
if(c != '%'){
putc(c, stdout);
continue;
}
gpr3++;
if(t == 's') {
uint32_t ptr = PowerPC::ppcState.gpr[r];
r++;
char cBis;
do {
ptr++;
putc(cBis, stdout);
} while (cBis != 0);
}
else if (t == '%'){
putc('%', stdout);
}
else if (t == '0'){
// Padded format strings : "%08x"
gpr3 += 2;
printf(formatStr, PowerPC::ppcState.gpr[r]);
r++;
}
else {
char formatStr[] = {'%', t};
printf(formatStr, PowerPC::ppcState.gpr[r]);
r++;
}
} while(c != 0);
}
m_end_block = true;
}
Because I edited the PowerPC interpreter, I had to disable the JIT but the Wii is a pretty modern console, my 7-year-old Intel CPU was pretty slow while trying to interpret the 729 Mhz PowerPC CPU of the Wii. It was unusable. I was not confident while trying to understand the JIT code so I just added a line to disable JIT on branch instruction to print_serial :
// In Source/Core/Core/PowerPC/Jit64/Jit_Branch.cpp
void Jit64::bx(UGeckoInstruction inst)
{
//...
FALLBACK_IF(js.op->branchTo == 0x801840dc);
//...
}
There are some slowdowns when the game tries to print a lot of stuff but at least it works !
<< RVL_SDK - EXI release build: Nov 30 2006 03:26:56 (0x4199_60831) >>
<< RVL_SDK - SI release build: Nov 30 2006 03:31:44 (0x4199_60831) >>
Revolution OS
Kernel built : Apr 24 2007 11:50:47
Console Type : NDEV 2.1
Firmware : 21.4.15 (3/3/2010)
Memory 88 MB
MEM1 Arena : 0x804f0fa0 - 0x817fcda0
MEM2 Arena : 0x90000800 - 0x933e0000
<< RVL_SDK - OS release build: Apr 24 2007 11:50:47 (0x4199_60831) >>
<< RVL_SDK - SC release build: Nov 30 2006 03:33:00 (0x4199_60831) >>
<< RVL_SDK - NAND release build: Nov 30 2006 03:32:57 (0x4199_60831) >>
<< RVL_SDK - NWC24 release build: May 10 2007 17:58:59 (0x4199_60831) >>
<< RVL_SDK - DVD release build: Apr 24 2007 11:44:29 (0x4199_60831) >>
<< NW4R - EF final build: Jun 8 2007 11:16:29 (0x4199_60831) >>
<< RVL_SDK - GX release build: Nov 30 2006 03:30:39 (0x4199_60831) >>
<< RVL_SDK - VI release build: Nov 30 2006 03:31:49 (0x4199_60831) >>
<< RVL_SDK - WPAD release build: May 17 2007 01:52:03 (0x4199_60831) >>
<< RVL_SDK - KPAD release build: Jun 5 2007 11:27:45 (0x4199_60831) >>
<< NW4R - G3D final build: Jun 8 2007 11:16:25 (0x4199_60831) >>
<< NW4R - LYT final build: Jun 8 2007 11:17:26 (0x4199_60831) >>
<< RVL_SDK - AI release build: Nov 30 2006 03:26:11 (0x4199_60831) >>
<< RVL_SDK - AX release build: Dec 18 2006 15:43:48 (0x4199_60831) >>
<< RVL_SDK - DSP release build: Nov 30 2006 03:26:46 (0x4199_60831) >>
<< NW4R - SND final build: Jun 8 2007 11:17:15 (0x4199_60831) >>
<< RVL_SDK - RFL release build: Jun 9 2007 17:25:33 (0x4199_60831) >>
|
2022-11-30 12:44:39
|
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|
https://philippegroarke.com/blog/2017/02/19/quicktip-understanding-16-byte-memory-alignment-detection/
|
When working with SIMD intrinsics, it helps to have a thorough understanding of computer memory. In this post, I hope to shed some light on a really simple but essential operation to figure out if memory is aligned at a 16 byte boundary.
When writing an SSE algorithm loop that transforms or uses an array, one would start by making sure the data is aligned on a 16 byte boundary. If not, a single “warmup pass” of the algorithm is usually performed to prepare for the main loop. Many programmers use a variant of the following line to find out if the array pointer is adequately aligned.
if (((intptr_t)array_pointer & 0xF) != 0) {
/* unaligned pre-pass */
}
So what is happening? I will use theoretical 8 bit pointers to explain the operation. Lets illustrate using pointers to the addresses 16 (0x10) and 92 (0x5C). 92 being unaligned.
16 92
0001 0000 | 0101 1100
We first cast the pointer to a intptr_t (the debate is up whether one should use uintptr_t instead). This allows us to use bitwise operations on the pointer itself.
Next, we bitwise multiply the address with 15 (0xF). This operation masks the higher bits of the memory address, except the last 4, like so.
16 92
0001 0000 | 0101 1100
0000 1111 | 0000 1111 & 0xF
---------------------
The cryptic if statement now becomes very clear and intuitive. We simply mask the upper portion of the address, and check if the lower 4 bits are zero. If they aren’t, the address isn’t 16 byte aligned and we need to pre-heat our SIMD loop.
|
2021-07-28 04:37:43
|
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|
https://math.stackexchange.com/questions/2359562/what-does-int-sindx-mean
|
# What does $\int \sin(dx)$ mean?
This is only about, how I came up with this weird idea.
I was considering about relationship between radius($r$),arc of the circle ($s$) and radian ($\theta$) such that;
$$\boxed{r/s=\theta}$$
And to convince myself completely, I wanted to try following method. When $s,\phi$ are very small like $\delta s$ and $\delta \phi$, we can assume that the triangle that $rsr$ with angle $\delta \phi$ that is;
So from the triangle, we can conclude that $$\sin\left(\frac{\delta \phi}{2}\right)=\dfrac{\delta s}{2r}$$ and while $\delta s,\delta \phi$ go to the $0$ we can take integral at both side.
Conclusion:
What does following mean?
$$\boxed{I=\displaystyle\int \sin(dx)}$$
1.
I considered that what if we take the integral to inside of $\sin(x)$?
so $I=\sin (x+C)$
2.
I've tried definition of riemann integral.
$$\displaystyle\int_a^b f(x)dx=\lim\limits_{n\to \infty}\displaystyle\sum_{k=0}^n f\left(a+k\dfrac{b-a}{n}\right)\left(\dfrac{b-a}{n}\right)$$
But what is the function? $f(dx)$ doesn't look like just $f(x)$ or I can try following but it doesn't make any sense to me, as well.
$$\displaystyle\int f(dx)=\int \dfrac{f(dx)}{dx}dx$$ so $U(x)=\dfrac{f(dx)}{dx}$, but I couldn't finish.
• In terms of Riemann sums, I imagine you'd have: $$\int_a^bf(dx)=\lim_{n\to\infty}\sum_{k=0}^nf\left(\frac{b-a}n\right)=\lim_{n\to\infty}(n+1)f\left(\frac{b-a}n\right)$$Though this is just a guess. – Simply Beautiful Art Jul 15 '17 at 12:09
• That's mostly meaningless – Hagen von Eitzen Jul 15 '17 at 12:10
• just an idea: probably (not sure) $\mathrm dx$ is defined in non-standard analysis in terms of infinitesimals. If this is the case then we can find a meaning for some expression of the kind $f(\mathrm dx)$. – Masacroso Jul 15 '17 at 12:14
• @HagenvonEitzen. Many ideas have been meaningless in the beginning, but later got a rigorous mathematical treatment, e.g. the Dirac $\delta$ "function". The idea in the question is not that stupid and actually can be given a meaning. – md2perpe Jul 15 '17 at 22:14
• The most natural value of $f(dx)$ is $f'(0) \, dx$. Generally, $f(x+dx) = f(x) + f'(x) \, dx$. Therefore, $U(x) = f'(0)$. – md2perpe Jul 15 '17 at 22:17
Perhaps this will help: for very small angles $\sin(x) = x$ is a very good approximation. You can use this to show: $\dfrac{\delta \phi}{2} =\dfrac{\delta s}{2r}$ which leads to $\delta \phi = \dfrac{\delta s}{r}$ and now you can integrate both sides to show $s=2\pi r$.
Note: I respectfully point out that arc-length is proportional to both radius and angle so: $s = r \phi$; I think you might have a typo in your first boxed equation.
But I don't think I answered the question... what could $\int \sin(dx)$ mean.
One possible way to look at what $\sin(dx)$ means could come from the definition of the derivative: $f'(x)=\lim_{dx \to 0} \left[ \frac {f(x+dx)-f(x)} {dx} \right]$
now take some liberty with the limit and move it to the whole equation level. Also, evaluate the equation at zero.
$\lim_{dx \to 0} \left[ f'(0)= \frac {f(0+dx)-f(0)} {dx} \right]$
And rearrange to isolate $f(dx)$.
$\lim_{dx \to 0} \left[ f(dx)=f(0)+f'(0) dx \right]$
So: $\lim_{dx \to 0} \left[ \sin(dx) = \sin(0)+\cos(0)dx = dx \right]$
Which gets us back to the approximation that $\sin(x) = x$ for very small angles.
With particular reference to the sector of circle given $$\boxed{r = s \cdot \theta}$$ is incorrect, chasing it could lead to weird results. $$\boxed{s = r\cdot \theta}$$ is correct, leading to correct result.
The text that you reproduced does not mention the "conclusion"
$$\int\sin(dx)$$ which is meaningless (there isn't even a variable $$x$$ in the explanation).
What you can write is
$$\sin\left(\frac{\delta \phi}{2}\right)\approx\frac{\delta \phi}{2}=\dfrac{\delta s}{2r}$$
and from this, replacing small increments by differentials,
$$S=\oint ds=\int_0^\theta r\,d\phi=r\theta.$$
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2020-01-28 04:03:55
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https://tex.stackexchange.com/questions/442548/how-to-divide-a-slide-in-beamer-into-two-columns-as-shown-in-figure
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# How to divide a slide in beamer into two columns as shown in figure
I'm wondering if someone can help me how to generate this figure using sharelatex.
• For the arrows, I would use tikz. You can put an entire itemize inside a node [text width=...]. – John Kormylo Jul 20 '18 at 20:49
• Can you make a minimal working example (MWE) to show us what you already tried? – samcarter_is_at_topanswers.xyz Jul 21 '18 at 11:06
• I guess people (and ducks and marmots) here would be more eager to help you if you would (a) show us what you have tried and (b) give feedback to the answers of your other questions by either saying what you think is missing or accepting them. And I agree that with @JohnKormylo that the upper part can be easily done with TikZ, and for the lower part you could either use columns or TikZ. – user121799 Jul 21 '18 at 14:38
• Since you have some responses below that seem to answer your question, please consider marking one of them as ‘Accepted’ by clicking on the tickmark below their vote count (see How do you accept an answer?). This shows which answer helped you most, and it assigns reputation points to the author of the answer (and to you!). It's part of this site's idea to identify good questions and answers through upvotes and acceptance of answers. – samcarter_is_at_topanswers.xyz Aug 8 '18 at 0:57
\documentclass{beamer}
\usepackage{tikz,bbm}
\begin{document}
\begin{frame}[t]{Population vs.\ sample based PCA}
\centering
\begin{tikzpicture}
\draw[latex-latex] (0,0) -- (0,1) -- (8,1) coordinate[midway](X) -- (8,0);
\draw (X) -- ++(0,1) node[above]{PCA};
\end{tikzpicture}
\begin{columns}
\begin{column}{0.6\textwidth}
\begin{itemize}
\item Population PCA
\item $x\in\mathbbm{R}^m$, random vector
\end{itemize}
\end{column}
\begin{column}{0.4\textwidth}
\begin{itemize}
\item Sample based PCA
\item $\mu,\Sigma$ not known
\end{itemize}
\end{column}
\end{columns}
\end{frame}
\end{document}
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2021-04-16 19:30:52
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https://physics.stackexchange.com/questions/513860/triangle-gauge-anomalies
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# Triangle gauge anomalies
In group theory, how we call this quantity $$$$A^{abc}=Tr(T_{L}^{a}\{T_{L}^{b},T_{L}^{c}\})$$$$
• d-coefficient. Its scale varies with representation. Physicists call it "anomaly coefficient". See this. – Cosmas Zachos Nov 14 at 15:00
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2019-12-16 02:41:42
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http://mathhelpforum.com/algebra/61373-please-explain.html
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(x – 2)^2
2. Originally Posted by Elli
(x – 2)^2
$(x-2)^2 = (x-2)(x-2) = x^2-2x-2x+4 = x^2-4x+4$
make two brackets then foil.
3. Originally Posted by Elli
(x – 2)^2
hi
it is like (a-b)^2 ^-whole square
(a-b)^2=a^2-2ab+b^2 (^power2)
(x-2)^2=x^2-2*x*2+2^2
(x-2)^2=x^2-4x+4
ok
4. ## Unless specifically asked to do foil
I would learn to use saranya's method ASAP. Saves you a ton of time on tests and on future problems.
5. ## Thank you!
Thank you for your help .. euclid2, petergunz and saranya
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2017-03-30 03:31:31
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https://codegolf.stackexchange.com/questions/175841/reciprocal-copycats/175853
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# Reciprocal copycats
Let $$\A\$$ be a positive integer consisting of $$\n\$$ decimal digits $$\d_1,d_2,...,d_n\$$. Let $$\B\$$ be another positive integer.
For the purpose of this challenge, we call $$\A\$$ a copycat of $$\B\$$ if there exists at least one list of positive integers $$\p_1,p_2,...,p_n\$$ such that:
$$\sum_{i=1}^{n}{{d_i}^{p_i}}=B$$
$$\A\$$ and $$\B\$$ are called reciprocal copycats if $$\A\$$ is a copycat of $$\B\$$ and $$\B\$$ is a copycat of $$\A\$$.
## Example
$$\526\$$ and $$\853\$$ are reciprocal copycats because:
$$5^3 + 2^9 + 6^3 = 853$$
and:
$$8^3 + 5^1 + 3^2 = 526$$
## The challenge
Given two positive integers $$\A\$$ and $$\B\$$, your task is to print or return a truthy value if $$\A\$$ and $$\B\$$ are reciprocal copycats or a falsy value otherwise.
## Clarifications and rules
• You may take $$\A\$$ and $$\B\$$ in any reasonable, unambiguous format (e.g. integers, strings, lists of digits, ...)
• $$\A\$$ and $$\B\$$ may be equal. If a number is a reciprocal copycat of itself, it belongs to A007532.
• Instead of truthy/falsy values, you may return two distinct consistent values.
• For $$\1\le A<1000\$$ and $$\1\le B<1000\$$, your code must complete in less than one minute. If it's taking too much time for higher values, it must however be able to solve them in theory.
• This is .
## Test cases
Truthy:
1 1
12 33
22 64
8 512
23 737
89 89
222 592
526 853
946 961
7 2401
24 4224
3263 9734
86 79424
68995 59227
32028 695345
Falsy:
1 2
3 27
9 24
24 42
33 715
33 732
222 542
935 994
17 2401
8245 4153
• Suggested case: 17 2401 -> false. I'm almost tripped on this. – Shieru Asakoto Nov 15 '18 at 5:46
# Brachylog, 19 bytes
ẹ{∧ℕ₁;?↔^}ᵐ².+ᵐ↔?∧≜
Try it online!
Outputs true. or false.
### Explanation
ẹ Split the numbers into lists of digits
{ }ᵐ² For each digit
∧ℕ₁ Let I be a strictly positive integer
;?↔^ Compute the digit to the power I (which is unknown currently)
. Call . the list of those new numbers
.+ᵐ Their mapped sum results…
↔? …in the reverse of the input
∧≜ Find if there effectively are values for the numbers in . to satisfy
these relationships
• @Arnauld Fixed at the cost of 1 byte. It failed because 2401 contained a 0 which didn't work with the way I checked that I was strictly positive (because I mapped it on both I and the digit to save bytes) – Fatalize Nov 13 '18 at 12:42
# Husk, 17 bytes
Λλ€⁰mΣΠTṪ^ḣ√⁰d)De
Try it online! Finishes all test cases under 1000 in about 11 seconds.
## Explanation
Λλ€⁰mΣΠTṪ^ḣ√⁰d)De Implicit inputs, say 12 and 33.
e Put into a list: [12,33]
D Duplicate: [12,33,12,33]
Λ Does this hold for all adjacent pairs:
(12,33 is checked twice but it doesn't matter)
For example, arguments are 33 and 12.
λ ) Anonymous function with arguments 33 (explicit) and 12 (implicit).
d Base-10 digits of implicit argument: [1,2]
ḣ√⁰ Range to square root of explicit argument: [1,2,3,4]
Ṫ^ Outer product with power: [[1,2],[1,4],[1,8],[1,16],[1,32]]
T Transpose: [[1,1,1,1,1],[2,4,8,16,32]]
Π Cartesian product: [[1,2],[1,4],...,[1,32]]
mΣ Map sum: [3,5,...,33]
€⁰ Is the explicit argument in this list? Yes.
## Why it works
If we have $$\B = d_1^{p_1} + \cdots + d_n^{p_n}\$$ where the $$\d_i\$$ are digits and $$\p_i\$$ are positive integers, then $$\d_i^{p_i} \leq B\$$ for all $$\i\$$, or equivalently $$\p_i \leq \log_{d_i} B\$$. We can ignore the case $$\d_i \leq 1\$$, since exponentiating $$\0\$$ or $$\1\$$ does not change it. In my program the search space is $$\1 \leq p_i \leq \sqrt{B}\$$ (to comply with the time restriction; I would use $$\1 \leq p_i \leq B\$$ otherwise), so if we have $$\\lfloor \log_{d_i} B \rfloor \leq \lfloor \sqrt{B} \rfloor\$$, then everything is fine. If $$\d_i \geq 3\$$, this holds for all natural numbers $$\B\$$, so the only dangerous case is $$\d_i = 2\$$. We have $$\\lfloor \log_2 B \rfloor > \lfloor \sqrt{B} \rfloor\$$ only for $$\B = 8\$$. In this case $$\2^3 = 8\$$, but the search only considers exponents $$\1\$$ and $$\2\$$. If the other number number $$\A\$$ contains the digit $$\2\$$, either it has other nonzero digits as well (so the exponent of $$\2\$$ cannot be $$\3\$$ in the sum), or $$\A = 2 \cdot 10^k\$$ for some $$\k\$$. In the latter case, $$\A\$$ is not a power of $$\8\$$, so it cannot be a copycat of $$\B\$$ anyway, and the program correctly returns a falsy value regardless of the other computation.
• Great answer which makes me want to learn Husk. Two questions: 1. the implicit argument is mentioned again after you introduce it. When is it used? 2. Could you elaborate on why this algorithm is equivalent to the one posed in the OP? – Jonah Nov 15 '18 at 4:28
• @Jonah 1. The digit function d takes the implicit argument. I clarified this in the explanation. 2. I added an argument for the program's correctness. – Zgarb Nov 15 '18 at 11:55
• Thank you... btw, the part that had confused me was "where does the list of all ones come from?".... rereading i now realize this is merely because all the powers of 1 are just one.... – Jonah Nov 15 '18 at 18:30
# Python 2, 102 bytes
lambda a,b:g(a,b)*g(b,a)
g=lambda a,b,e=1:b==a<1or(b>0<=b-e>=0<a)and(g(a/10,b-(a%10)**e)or g(a,b,e+1))
Try it online!
# 05AB1E, 26 22 bytes
εVтLIàgãεYSym}OIyKå}˜P
Takes the input as a list (i.e. [526,853]).
Similar as my old answer below, except that the [1,n] list is hardcoded to [1,100], and it creates the cartesian list twice, once for each input-mapping, which is the main bottleneck in terms of performance.
Old 26 bytes answer that's better for performance:
Z©bgL®gãUεVXεYSym}OsN>èå}P
In this version I traded in some bytes to make the performance a lot better so it can run [1,1000] with ease. Test cases containing numbers in the range [1,9999] are done in about a second on TIO. Test cases in the range [10000,99999] in about 10-15 seconds on TIO. Above that it will timeout.
Explanation:
Z # Push the max of the (implicit) input-list (without popping)
# i.e. [526,853] → 853
© # Store it in the register (without popping)
b # Convert to binary
# i.e. 853 → 1101010101
g # Take its length
# i.e. 1101010101 → 10
L # Pop and push a list [1, n]
# i.e. 10 → [1,2,3,4,5,6,7,8,9,10]
® # Push the max from the register
g # Take its length
# i.e. 853 → 3
ã # Cartesian product the list that many times
# i.e. [1,2,3,4,5,6,7,8,9,10] and 3
# → [[1,1,1],[1,1,2],[1,1,3],...,[10,10,8],[10,10,9],[10,10,10]]
U # Pop and store it in variable X
ε } # Map both values of the input list:
V # Store the current value in variable Y
Xε } # Map y over the numbers of variable X
Y # Push variable Y
S # Convert it to a list of digits
# i.e. 526 → [5,2,6]
ym # Take each digit to the power of the current cartesian product sublist
# i.e. [5,2,6] and [3,9,3] → [125,512,216]
O # Take the sum of each inner list
# i.e. [[5,2,6],[5,2,36],[5,2,216],...,[125,512,216],...]
# → [13,43,223,...,853,...]
s # Swap to push the (implicit) input
N> # Push the index + 1
# i.e. 0 → 1
è # Index into the input-list (with automatic wraparound)
# i.e. [526,853] and 1 → 853
å # Check if it's in the list of sums
# i.e. [13,43,223,...,853,...] and 853 → 1
P # Check if it's truthy for both both (and output implicitly)
# i.e. [1,1] → 1
a#b=a!b&&b!a
a!b|a<1=b==0|b<1=b>1|1<2=or[div a 10!(b-mod a 10^e)|e<-[1..b+1]]
Try it online!
# Perl 6, 87 84 69 bytes
-15 bytes thanks to nwellnhof!
{!grep {!grep $^b,[X+] 0,|map (*X**1..$b.msb+1),$^a.comb},.[0,1,1,0]} Try it online! Anonymous code block that returns True or False. ### Explanation: {!grep {!grep$^b,[X+] 0,|map (*X**1..$b.msb+1),$^a.comb},.[0,1,1,0]}
{ } # Anonymous code block
!grep # None of:
.[0,1,1,0] # The input and the input reverse
{!grep # None of
[X+] # All possible sums of
0,| # 0 (this is to prevent single digit numbers being crossed with themself)
map ,$^a.comb # Each digit mapped to (*X** ) # The power of 1..$b.msb+1 # All of 1 to the most significant bit of b plus 1
# This could just be b+1, but time constraints...
\$^b, # Is equal to b
• @Arnauld, A Junction is Truthy/Falsey, as I've shown by using the boolify operator before outputting. I golfed it to something else anyway, though I could save a byte if I could output a truthy value for false and vice-versa...? – Jo King Nov 13 '18 at 11:40
• Thanks for the clarification. About the truthy/falsy inversion: I'd rather say no. – Arnauld Nov 13 '18 at 11:45
# JavaScript (Node.js), 11692898683 77 bytes
a=>b=>(G=(c,g,f=h=g%10)=>g?c>f&f>1&&G(c,g,h*f)||G(c-f,g/10|0):!c)(a,b)&G(b,a)
Try it online!
Expect input as (A)(B).
• Strings are fine. (I've clarified the input format in the challenge.) – Arnauld Nov 13 '18 at 11:41
• @Arnauld Oh I've just found a method not using string but also 108 bytes. – Shieru Asakoto Nov 13 '18 at 11:48
# J, 56 bytes
h~*h=.4 :'x e.+/|:>,{x 4 :''<y&*^:(x&>)^:a:y''"+"."+":y'
Try it online!
Yay, nested explicit definition!
### How it works
powers =. 4 :'<y&*^:(x&>)^:a:y' Explicit aux verb. x = target, y = digit
y Starting from y,
y&*^: ^:a: collect all results of multiplying y
(x&>) until the result is at least x
< Box it.
h=.4 :'x e.+/|:>,{x powers"+"."+":y' Explicit aux verb. x, y = two input numbers
"."+":y Digits of y
x powers"+ Collect powers of digits of y under x
{ Cartesian product of each item
+/|:>, Format correctly and compute the sums
x e. Does x appear in the list of sums?
h~*h Tacit main verb. x, y = two input numbers
Since h tests the condition in only one direction,
test again the other way around (~) and take the AND.
# Python 2, 149147143139132118108107106 105 bytes
lambda a,b:g(a,b)*g(b,a)
g=lambda a,b:any(g(a/10,b-(a%10)**-~i)for i in(a*b>0)*range(len(bin(b))))or b==0
Try it online!
-4 bytes, thanks to Vedant Kandoi
• >0 can be removed. not a:a<1. b==0:b<1 – Vedant Kandoi Nov 13 '18 at 11:37
• @VedantKandoi Thanks, though b<0 doesn't work – TFeld Nov 13 '18 at 11:41
# J, 68 bytes
I thought J would perform quite well here, but it ended up being tougher than I expected and would love any suggestions for further golfing...
g=.#@#:@[
1 1-:[:(([:+./[=1#.]^"#.1+g#.inv[:i.g^#@])"."0@":)/"1],:|.
Try it online!
NOTE: we subtract 3 chars from the TIO count there since f=. on the main function doesn't count
## ungolfed
1 1 -: [: (([: +./ [ = 1 #. ] ^"#. 1 + g #.inv [: i. g ^ #@]) "."0@":)/"1 ] ,: |.
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2019-10-16 14:08:33
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https://www.electro-tech-online.com/threads/waiting-for-input-while-checking-temprature.99309/
|
waiting for input while checking temprature?
Status
Not open for further replies.
dawson
New Member
I currently use the following code to read the temp from a ds1820, I have it displaying the current temp all the time but I have a menu so if a button is pressed it brings up the menu instead of displaying the temp.
The problem is that the read_temp() function has delays so the switch has to be pressed at a certain time, here is the code:
Code:
void read_temp() {
Ow_Reset(&PORTB, 5); // Onewire reset signal
Ow_Write(&PORTB, 5, 0xCC); // Issue command SKIP_ROM
Ow_Write(&PORTB, 5, 0x44); // Issue command CONVERT_T
Delay_ms(600);
// If this delay is less than 500ms, you will see the first reading on LCD
//85C which is (if you remember from my article on DS1820)
//a power-on-reset value.
Ow_Reset(&PORTB, 5);
Ow_Write(&PORTB, 5, 0xCC); // Issue command SKIP_ROM
// Then read Byte 1 from Scratchpad and shift 8 bit left and add the Byte 0
temp_value = (Ow_Read(&PORTB, 5) << 8) + temp_value;
//--- Format and display result on Lcd
Display_Temperature(temp_value);
}
void main() {
CMCON |= 7; // Disable Comparators
Lcd_Init(); // Initialize LCD
Lcd_Cmd(_LCD_CLEAR); // Clear LCD
Lcd_Cmd(_LCD_CURSOR_OFF); // Turn cursor off
Lcd_Cmd(_LCD_CLEAR); // Clear display
Lcd_Out(1, 3, "Temperature: ");
// Print degree character, 'C' for Centigrades
Lcd_Chr(2,11,223);
// different LCD displays have different char code for degree
// if you see greek alpha letter try typing 178 instead of 223
Lcd_Chr(2,12,'C');
//--- main loop
do {
if(Button(&PORTA,2, 1, 0)) {
}
} while (1);
}
How can I have it so that it will still loop through checking the temp but will goto the menu as soon as the switch is pressed?
Edit: Forgot to mention Im using the pic16f628
Last edited:
dawson
New Member
thanks, will have a search for using interupts. Anyone have any good resources?
birdman0_o
Active Member
It would help if you said which uC. Most, if not all? pic16f's have PORTB interrupts on change, look into that
dawson
New Member
uC? Im using pic16f628. I have had a look for interrupts but cant really find much can anyone help?
birdman0_o
Active Member
Port B interrupts, the datasheet provides plenty of info about how to set them up!
Mr RB
Well-Known Member
Just remove (or shorten) the 600mS delay. If you read the scratchpad too soon (before conversion is completed) if just reads the previous scratchpad value. And if you tell it do a conversion while it is still doing one it will ignore the new request.
dawson
New Member
I will give that a try since I am not getting very far with interrupts lol, thanks
dawson
New Member
thanks ill take a look
Diver300
Well-Known Member
You can get the delay routine to read the button.
All the other operations of a DS1820 are very quick, so they won't introduce too big a lag.
dawson
New Member
diver300, can you explain that please i dont really understand
Diver300
Well-Known Member
When reading the DS18B20, the simplest routine is something like this:-
Code:
[U]Microcontroller[/U] [U]DS18B20[/U]
Reset Presence pulse
Skip Rom command (0xCC)
Convert Temp (0x44)
Wait for 750 ms
Reset Presence pulse
Skip Rom command (0xCC)
Read scratchpad (0xBE) Temperature
(You don't have to read the rest of the scratchpad. The microcontroller can stop after it has read the temperature)
The point is that the routine can be split into 3 parts:-
1) The communication bit before the 750 ms pause
2) The 750 ms pause
3) The communication bit after the 750 ms pause
The two communication parts are very quick. They are so quick that it doesn't matter if you don't look at the pushbutton during that time.
The 750 ms pause is what makes the pushbutton not respond. If you make the pause code read the pushbutton lots of times, it will still be a perfectly good pause. It really doesn't matter if you pause a bit too long. If the pushbutton is pressed you can abandon the temperature reading and start a new reading when you have dealt with the pushbutton.
It does mean that you have to modify the read_temp() code.
Are you using the DS18B20 with parasite power? The suggestions from Mr RB will only work if there is a separate power connection.
Last edited:
birdman0_o
Active Member
Great advice diver! Do you happen to have corresponding code though hanging around somewhere?
Thanks
Gayan Soyza
Active Member
As diver said set an push button press flag bit inside the 750mS routine if the button was pressed & check the flag bit before updating or reading the temperature.
AtomSoft
Well-Known Member
As i said a few times just check withing your code a few times. Interrupts are way better but since your LCD was on PORTB already it would require a change.
Your writing in MikroC (PRO) right? If you want... rearrange the LCD to another place and ill see if i can help you write some interrupt code.
free up At least RB0
Last edited:
dawson
New Member
Thanks for clearing that up diver i think I understand what you mean, I will give it a try. I am currentyl using the DS18S20 but may switch to the DS18B20 to use the 12 bit res
Atomsoft, thanks for the generous offer, I will see what I can do and might take you up on your offer.
Last edited:
AtomSoft
Well-Known Member
ok Ill be here if anything
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2021-10-16 09:20:07
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|
http://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/177/2/a/d/
|
# Properties
Label 177.2.a.d Level 177 Weight 2 Character orbit 177.a Self dual yes Analytic conductor 1.413 Analytic rank 0 Dimension 3 CM no Inner twists 1
# Related objects
## Newspace parameters
Level: $$N$$ $$=$$ $$177 = 3 \cdot 59$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 177.a (trivial)
## Newform invariants
Self dual: yes Analytic conductor: $$1.41335211578$$ Analytic rank: $$0$$ Dimension: $$3$$ Coefficient field: 3.3.229.1 Defining polynomial: $$x^{3} - 4 x - 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$
## $q$-expansion
Coefficients of the $$q$$-expansion are expressed in terms of a basis $$1,\beta_1,\beta_2$$ for the coefficient ring described below. We also show the integral $$q$$-expansion of the trace form.
$$f(q)$$ $$=$$ $$q + \beta_{1} q^{2} - q^{3} + ( 1 + \beta_{2} ) q^{4} + ( -1 + \beta_{1} - \beta_{2} ) q^{5} -\beta_{1} q^{6} + ( 3 + \beta_{1} ) q^{7} + q^{8} + q^{9} +O(q^{10})$$ $$q + \beta_{1} q^{2} - q^{3} + ( 1 + \beta_{2} ) q^{4} + ( -1 + \beta_{1} - \beta_{2} ) q^{5} -\beta_{1} q^{6} + ( 3 + \beta_{1} ) q^{7} + q^{8} + q^{9} + ( 2 - 2 \beta_{1} + \beta_{2} ) q^{10} + ( -1 - \beta_{1} - \beta_{2} ) q^{11} + ( -1 - \beta_{2} ) q^{12} + ( 1 - \beta_{1} - \beta_{2} ) q^{13} + ( 3 + 3 \beta_{1} + \beta_{2} ) q^{14} + ( 1 - \beta_{1} + \beta_{2} ) q^{15} + ( -2 + \beta_{1} - 2 \beta_{2} ) q^{16} + ( 2 - 2 \beta_{1} + 3 \beta_{2} ) q^{17} + \beta_{1} q^{18} + ( 2 - \beta_{2} ) q^{19} + ( -3 + \beta_{1} ) q^{20} + ( -3 - \beta_{1} ) q^{21} + ( -4 - 2 \beta_{1} - \beta_{2} ) q^{22} + ( -2 \beta_{1} - \beta_{2} ) q^{23} - q^{24} + ( -3 \beta_{1} + \beta_{2} ) q^{25} + ( -4 - \beta_{2} ) q^{26} - q^{27} + ( 4 + 2 \beta_{1} + 3 \beta_{2} ) q^{28} + ( -3 + \beta_{1} + 2 \beta_{2} ) q^{29} + ( -2 + 2 \beta_{1} - \beta_{2} ) q^{30} + ( 5 - \beta_{1} + 2 \beta_{2} ) q^{31} + ( -1 - 4 \beta_{1} + \beta_{2} ) q^{32} + ( 1 + \beta_{1} + \beta_{2} ) q^{33} + ( -3 + 5 \beta_{1} - 2 \beta_{2} ) q^{34} + ( -1 + \beta_{1} - 2 \beta_{2} ) q^{35} + ( 1 + \beta_{2} ) q^{36} + ( -2 - 2 \beta_{1} - \beta_{2} ) q^{37} + ( -1 + \beta_{1} ) q^{38} + ( -1 + \beta_{1} + \beta_{2} ) q^{39} + ( -1 + \beta_{1} - \beta_{2} ) q^{40} + ( -1 + 3 \beta_{1} - 2 \beta_{2} ) q^{41} + ( -3 - 3 \beta_{1} - \beta_{2} ) q^{42} + ( 1 + 5 \beta_{1} - 3 \beta_{2} ) q^{43} + ( -5 - 3 \beta_{1} ) q^{44} + ( -1 + \beta_{1} - \beta_{2} ) q^{45} + ( -7 - \beta_{1} - 2 \beta_{2} ) q^{46} + ( 5 - \beta_{1} + 4 \beta_{2} ) q^{47} + ( 2 - \beta_{1} + 2 \beta_{2} ) q^{48} + ( 5 + 6 \beta_{1} + \beta_{2} ) q^{49} + ( -8 + \beta_{1} - 3 \beta_{2} ) q^{50} + ( -2 + 2 \beta_{1} - 3 \beta_{2} ) q^{51} + ( -3 - 3 \beta_{1} + 2 \beta_{2} ) q^{52} + ( 1 - 5 \beta_{1} + \beta_{2} ) q^{53} -\beta_{1} q^{54} + ( 1 + \beta_{1} - \beta_{2} ) q^{55} + ( 3 + \beta_{1} ) q^{56} + ( -2 + \beta_{2} ) q^{57} + ( 5 - \beta_{1} + \beta_{2} ) q^{58} + q^{59} + ( 3 - \beta_{1} ) q^{60} + ( 1 + \beta_{1} + 4 \beta_{2} ) q^{61} + ( -1 + 7 \beta_{1} - \beta_{2} ) q^{62} + ( 3 + \beta_{1} ) q^{63} + ( -7 - 2 \beta_{1} ) q^{64} + ( -1 + 3 \beta_{1} - 3 \beta_{2} ) q^{65} + ( 4 + 2 \beta_{1} + \beta_{2} ) q^{66} + ( 5 + \beta_{1} + 5 \beta_{2} ) q^{67} + ( 9 - \beta_{1} - \beta_{2} ) q^{68} + ( 2 \beta_{1} + \beta_{2} ) q^{69} + ( 1 - 3 \beta_{1} + \beta_{2} ) q^{70} + ( 9 - 3 \beta_{1} + \beta_{2} ) q^{71} + q^{72} + ( 1 - 3 \beta_{1} - 4 \beta_{2} ) q^{73} + ( -7 - 3 \beta_{1} - 2 \beta_{2} ) q^{74} + ( 3 \beta_{1} - \beta_{2} ) q^{75} + ( -1 - \beta_{1} + 3 \beta_{2} ) q^{76} + ( -7 - 5 \beta_{1} - 4 \beta_{2} ) q^{77} + ( 4 + \beta_{2} ) q^{78} + ( 1 - 3 \beta_{1} + \beta_{2} ) q^{79} + ( 8 - 4 \beta_{1} + \beta_{2} ) q^{80} + q^{81} + ( 7 - 3 \beta_{1} + 3 \beta_{2} ) q^{82} + ( 1 - 5 \beta_{1} + 6 \beta_{2} ) q^{83} + ( -4 - 2 \beta_{1} - 3 \beta_{2} ) q^{84} + ( -12 + 6 \beta_{1} - \beta_{2} ) q^{85} + ( 12 - 2 \beta_{1} + 5 \beta_{2} ) q^{86} + ( 3 - \beta_{1} - 2 \beta_{2} ) q^{87} + ( -1 - \beta_{1} - \beta_{2} ) q^{88} + ( -9 + 3 \beta_{1} - 4 \beta_{2} ) q^{89} + ( 2 - 2 \beta_{1} + \beta_{2} ) q^{90} + ( -1 - 3 \beta_{1} - 4 \beta_{2} ) q^{91} + ( -5 - 5 \beta_{1} + \beta_{2} ) q^{92} + ( -5 + \beta_{1} - 2 \beta_{2} ) q^{93} + ( 1 + 9 \beta_{1} - \beta_{2} ) q^{94} + ( 2 \beta_{1} - 3 \beta_{2} ) q^{95} + ( 1 + 4 \beta_{1} - \beta_{2} ) q^{96} + ( 5 - 5 \beta_{1} + \beta_{2} ) q^{97} + ( 19 + 6 \beta_{1} + 6 \beta_{2} ) q^{98} + ( -1 - \beta_{1} - \beta_{2} ) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3q - 3q^{3} + 2q^{4} - 2q^{5} + 9q^{7} + 3q^{8} + 3q^{9} + O(q^{10})$$ $$3q - 3q^{3} + 2q^{4} - 2q^{5} + 9q^{7} + 3q^{8} + 3q^{9} + 5q^{10} - 2q^{11} - 2q^{12} + 4q^{13} + 8q^{14} + 2q^{15} - 4q^{16} + 3q^{17} + 7q^{19} - 9q^{20} - 9q^{21} - 11q^{22} + q^{23} - 3q^{24} - q^{25} - 11q^{26} - 3q^{27} + 9q^{28} - 11q^{29} - 5q^{30} + 13q^{31} - 4q^{32} + 2q^{33} - 7q^{34} - q^{35} + 2q^{36} - 5q^{37} - 3q^{38} - 4q^{39} - 2q^{40} - q^{41} - 8q^{42} + 6q^{43} - 15q^{44} - 2q^{45} - 19q^{46} + 11q^{47} + 4q^{48} + 14q^{49} - 21q^{50} - 3q^{51} - 11q^{52} + 2q^{53} + 4q^{55} + 9q^{56} - 7q^{57} + 14q^{58} + 3q^{59} + 9q^{60} - q^{61} - 2q^{62} + 9q^{63} - 21q^{64} + 11q^{66} + 10q^{67} + 28q^{68} - q^{69} + 2q^{70} + 26q^{71} + 3q^{72} + 7q^{73} - 19q^{74} + q^{75} - 6q^{76} - 17q^{77} + 11q^{78} + 2q^{79} + 23q^{80} + 3q^{81} + 18q^{82} - 3q^{83} - 9q^{84} - 35q^{85} + 31q^{86} + 11q^{87} - 2q^{88} - 23q^{89} + 5q^{90} + q^{91} - 16q^{92} - 13q^{93} + 4q^{94} + 3q^{95} + 4q^{96} + 14q^{97} + 51q^{98} - 2q^{99} + O(q^{100})$$
Basis of coefficient ring in terms of a root $$\nu$$ of $$x^{3} - 4 x - 1$$:
$$\beta_{0}$$ $$=$$ $$1$$ $$\beta_{1}$$ $$=$$ $$\nu$$ $$\beta_{2}$$ $$=$$ $$\nu^{2} - 3$$
$$1$$ $$=$$ $$\beta_0$$ $$\nu$$ $$=$$ $$\beta_{1}$$ $$\nu^{2}$$ $$=$$ $$\beta_{2} + 3$$
## Embeddings
For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.
For more information on an embedded modular form you can click on its label.
Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1.1
−1.86081 −0.254102 2.11491
−1.86081 −1.00000 1.46260 −3.32340 1.86081 1.13919 1.00000 1.00000 6.18421
1.2 −0.254102 −1.00000 −1.93543 1.68133 0.254102 2.74590 1.00000 1.00000 −0.427229
1.3 2.11491 −1.00000 2.47283 −0.357926 −2.11491 5.11491 1.00000 1.00000 −0.756981
$$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles
## Atkin-Lehner signs
$$p$$ Sign
$$3$$ $$1$$
$$59$$ $$-1$$
## Inner twists
This newform does not admit any (nontrivial) inner twists.
## Twists
By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 177.2.a.d 3
3.b odd 2 1 531.2.a.d 3
4.b odd 2 1 2832.2.a.t 3
5.b even 2 1 4425.2.a.w 3
7.b odd 2 1 8673.2.a.s 3
12.b even 2 1 8496.2.a.bl 3
By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
177.2.a.d 3 1.a even 1 1 trivial
531.2.a.d 3 3.b odd 2 1
2832.2.a.t 3 4.b odd 2 1
4425.2.a.w 3 5.b even 2 1
8496.2.a.bl 3 12.b even 2 1
8673.2.a.s 3 7.b odd 2 1
## Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator $$T_{2}^{3} - 4 T_{2} - 1$$ acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(177))$$.
## Hecke characteristic polynomials
$p$ $F_p(T)$
$2$ $$1 + 2 T^{2} - T^{3} + 4 T^{4} + 8 T^{6}$$
$3$ $$( 1 + T )^{3}$$
$5$ $$1 + 2 T + 10 T^{2} + 18 T^{3} + 50 T^{4} + 50 T^{5} + 125 T^{6}$$
$7$ $$1 - 9 T + 44 T^{2} - 142 T^{3} + 308 T^{4} - 441 T^{5} + 343 T^{6}$$
$11$ $$1 + 2 T + 22 T^{2} + 48 T^{3} + 242 T^{4} + 242 T^{5} + 1331 T^{6}$$
$13$ $$1 - 4 T + 32 T^{2} - 78 T^{3} + 416 T^{4} - 676 T^{5} + 2197 T^{6}$$
$17$ $$1 - 3 T + 8 T^{2} - 4 T^{3} + 136 T^{4} - 867 T^{5} + 4913 T^{6}$$
$19$ $$1 - 7 T + 68 T^{2} - 270 T^{3} + 1292 T^{4} - 2527 T^{5} + 6859 T^{6}$$
$23$ $$1 - T + 42 T^{2} + 18 T^{3} + 966 T^{4} - 529 T^{5} + 12167 T^{6}$$
$29$ $$1 + 11 T + 96 T^{2} + 564 T^{3} + 2784 T^{4} + 9251 T^{5} + 24389 T^{6}$$
$31$ $$1 - 13 T + 130 T^{2} - 778 T^{3} + 4030 T^{4} - 12493 T^{5} + 29791 T^{6}$$
$37$ $$1 + 5 T + 92 T^{2} + 384 T^{3} + 3404 T^{4} + 6845 T^{5} + 50653 T^{6}$$
$41$ $$1 + T + 84 T^{2} + 156 T^{3} + 3444 T^{4} + 1681 T^{5} + 68921 T^{6}$$
$43$ $$1 - 6 T + 38 T^{2} + 76 T^{3} + 1634 T^{4} - 11094 T^{5} + 79507 T^{6}$$
$47$ $$1 - 11 T + 104 T^{2} - 538 T^{3} + 4888 T^{4} - 24299 T^{5} + 103823 T^{6}$$
$53$ $$1 - 2 T + 70 T^{2} - 270 T^{3} + 3710 T^{4} - 5618 T^{5} + 148877 T^{6}$$
$59$ $$( 1 - T )^{3}$$
$61$ $$1 + T + 82 T^{2} + 220 T^{3} + 5002 T^{4} + 3721 T^{5} + 226981 T^{6}$$
$67$ $$1 - 10 T + 82 T^{2} - 556 T^{3} + 5494 T^{4} - 44890 T^{5} + 300763 T^{6}$$
$71$ $$1 - 26 T + 406 T^{2} - 4116 T^{3} + 28826 T^{4} - 131066 T^{5} + 357911 T^{6}$$
$73$ $$1 - 7 T + 78 T^{2} - 304 T^{3} + 5694 T^{4} - 37303 T^{5} + 389017 T^{6}$$
$79$ $$1 - 2 T + 206 T^{2} - 348 T^{3} + 16274 T^{4} - 12482 T^{5} + 493039 T^{6}$$
$83$ $$1 + 3 T + 50 T^{2} + 350 T^{3} + 4150 T^{4} + 20667 T^{5} + 571787 T^{6}$$
$89$ $$1 + 23 T + 358 T^{2} + 3816 T^{3} + 31862 T^{4} + 182183 T^{5} + 704969 T^{6}$$
$97$ $$1 - 14 T + 266 T^{2} - 2514 T^{3} + 25802 T^{4} - 131726 T^{5} + 912673 T^{6}$$
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2020-10-22 13:05:57
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https://www.codecogs.com/library/engineering/thermodynamics/radiation/energy.php
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I have forgotten
• https://me.yahoo.com
COST (GBP)
0.75
0.00
0
energy
Computes the total energy radiated by a body with given parameters.
Controller: CodeCogs
Contents
C++
Excel
Energy
doubleenergy( double T double e = 1.0 )[inline]
This module calculates the total energy radiated by a body per unit surface area in unit time.
The total radiative energy of a black body is given by the Stefan-Boltzmann law
where is the radiative intensity of the black body.
In practice, the following formula due to Kirchoff is used
where is the emissivity constant of the black body , is the emissivity factor of the body and is its absolute temperature.
Example 1
The following example calculates the total radiative energy emitted by the Wolfram filament of an incandescent light bulb at 3573.16 degrees Kelvin.
#include <codecogs/engineering/heat_transfer/radiation/energy.h>
#include <stdio.h>
int main()
{
// the temperature of the Wolfram filament
double T = 3573.16;
// emissivity factor of the filament
double e = 0.39;
// display the total radiative energy
printf("Energy = %.5lf kW per sq. meter\n",
return 0;
}
Output
Energy = 3603.96794 kW per sq. meter
Note
A table with the emissivity factors of various materials at different temperatures can be found at the following link http://www.monarchserver.com/TableofEmissivity.pdf
References
Dan Stefanescu, Mircea Marinescu - "Termotehnica"
Parameters
T the absolute temperature of the body (Kelvin) e Default value = 1.0
Returns
the total radiative energy emitted by the body (Watt per square meter)
Authors
Grigore Bentea, Lucian Bentea (November 2006)
Source Code
Source code is available when you buy a Commercial licence.
Not a member, then Register with CodeCogs. Already a Member, then Login.
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2021-05-08 10:58:31
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|
https://www.ovito.org/docs/current/reference/pipelines/modifiers/cluster_analysis.html
|
# Cluster analysis¶
This modifier decomposes the particles into disconnected groups (so-called clusters) based on the selected neighboring criterion. The neighboring criterion can be distance-based (cutoff range) or topology-based (bond network).
A cluster is defined as a set of connected particles, each of which is within the (indirect) reach of the other particles in the same cluster. Thus, any two particles from the same cluster are connected by a continuous path consisting of steps that fulfill the selected neighboring criterion. Conversely, two particles will belong to different clusters if there is no such continuous path connecting the two particles on the neighbor graph.
Input
Output
## Connectivity criterion¶
You can choose between two clustering modes: In case of the distance-based mode, two particles are considered connected if they are within a specified proximity range of each other. In case of the bond-based mode, two particles are considered connected if there exists a bond between them. Note that particles not connected to any other particle will each form a single-particle cluster by itself.
## Cluster numbering¶
The clusters identified by the modifier are given numeric identifiers ranging from 1 to N, the total number of clusters. The algorithm assigns each input particle to one of these clusters and outputs this information as a new particle property named Cluster. Note that the ordering of clusters is arbitrary by default and will generally depend on the storage order of the input particles. You can, however, activate the option Sort clusters by size to request the sorting of cluster IDs by descending particle count. This option guarantees that the first cluster (ID 1) will be the largest one in the system, i.e. the one containing the most particles.
## Calculation of centers of mass¶
The modifier provides the option to compute the center of mass of each cluster. The coordinates will be output as an additional column in the generated clusters table (see below). The center of mass of clusters cut by a periodic simulation cell boundary will be correctly computed. However, if the extent of a cluster is infinite in the sense that it reconnects to itself through the periodic boundaries of the simulation domain, the results will be undefined. OVITO 3.2 and later take into account the per-particle masses when calculating the center of mass of a cluster. The mass information will be taken from the Mass property of individual particles (if present) or from the mass value set for each particle type. If neither the Mass particle property is present nor at least one particle type with a positive mass, then the algorithm assumes that all particles to have the same uniform weight.
## Calculation of gyration radius and gyration tensor¶
Furthermore, the modifier can compute the radius of gyration of each cluster as well as the gyration tensor. Both quantities will appear as additional columns in the generated table of clusters. The symmetric gyration tensor has six independent components: xx, yy, zz, xy, xz, yz (in simulation units of length squared). The data table is accessible in the data inspector panel:
The calculation of the radius of gyration and the gyration tensor in OVITO follows the compute gyration command of the LAMMPS simulation code. It takes into account the individual particle masses (if present) or the masses of the particle types (if set).
## Unwrapping of particle coordinates¶
The modifier provides the option to “unwrap” the coordinates of particles belonging to the same cluster, mapping them from inside the periodic simulation domain to outside in order for the cluster to appear as a contiguous object. Note that the unwrapping will yield meaningful results only for finite clusters. It will lead to undefined results for infinite clusters that are connected to themselves through a periodic cell boundary.
## Coloring option¶
The modifier option Color particles by cluster gives each identified cluster a unique random color and colors the particles according to the clusters they belong to. It helps to quickly visualize the results of the clustering algorithm.
## Restriction to selected particles¶
The option Use only selected particles restricts the clustering algorithm to the set of currently selected particles. Unselected particles will be treated as if they do not exist and will be assigned the special cluster ID 0.
## Exporting computation results¶
Total number of clusters
To export the total number of clusters found by the modifier to a text file (possibly as a function of time), use OVITO’s standard file export function. Select the output format Table of values and make sure that the ClusterAnalysis.cluster_count global attribute is selected for export.
Size of the largest clusters
The modifier also outputs the global attribute ClusterAnalysis.largest_size to report the number of particles in the largest cluster (only if the sort-by-size option is used). This information can be exported from OVITO in the same way as explained above.
Particle assignment to clusters
To export the list of particles belonging to each cluster to a text file, use OVITO’s file export function. Choose the output file format XYZ and mark the Particle Identifier and the Cluster properties for export. This will yield a text file containing each particle’s cluster ID.
Cluster size list and centers of mass
The modifiers outputs the list of identified clusters as a data table, which consists of one row per cluster and columns for the cluster size (number of particles), center of mass and radius of gyration (if their calculation is enabled). You can open this table in the data inspector panel of OVITO by pressing the button Show list of clusters. The data inspector panel provides a function for exporting the table data to a text file.
Cluster size distribution
Since the cluster table generated by the modifier contains each cluster’s size, you can subsequently apply OVITO’s Histogram to the Cluster Size column of that table to calculate the cluster size distribution.
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2021-07-27 21:59:19
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https://byjus.com/questions/rewrite-by-changing-the-voice-of-the-following-sarahs-bag-was-stolen-in-the-train/
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Rewrite By Changing The Voice Of The Following: Sarah’s Bag Was Stolen In The Train.
The given sentence – Sarah’s Bag Was Stolen In The Train. It is in the passive voice.
Active voice — Somebody stole Sarah’s bag on the train.
Explore more such questions and answers at BYJU’S.
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2021-10-19 01:30:32
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http://mathhelpforum.com/calculus/37026-trapezoidal-rule-uneven-subintervals.html
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# Thread: Trapezoidal Rule with uneven subintervals
1. ## Trapezoidal Rule with uneven subintervals
This is given:
f(1)= 2
f(5)= 10
f(8)= 13
f(12)= 17
Use trapezoidal approximation to find the area of the curve described by the function values above.
I understand that I need to find the area of all the trapezoids manually. I cannot apply the normal rule because the subintervals are different.
I used the height as the difference between 1 and 5 and the bases as 2 and 10, whcih plugged into the formula for the area of a trapezoid is $\frac{1}{2}$( 2 + 10).
I followed this pattern but my answer was clearly off. It was WAY too big.
So...how do I solve this problem?
2. Originally Posted by Truthbetold
This is given:
f(1)= 2
f(5)= 10
f(8)= 13
f(12)= 17
Use trapezoidal approximation to find the area of the curve described by the function values above.
I understand that I need to find the area of all the trapezoids manually. I cannot apply the normal rule because the subintervals are different.
I used the height as the difference between 1 and 5 and the bases as 2 and 10, whcih plugged into the formula for the area of a trapezoid is $\frac{1}{2}$( 2 + 10).
I followed this pattern but my answer was clearly off. It was WAY too big.
So...how do I solve this problem?
Using trapesoid rule area from $1$ to $5$ is $4 \times \frac{2+10}{2}=24$.
area from $5$ to $8$ is $3 \times \frac{10+13}{2}=34.5$
area from $8$ to $12$ is $4 \times \frac{13+17}{2}=60.$
RonL
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2013-12-18 22:50:17
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http://www.eng-tips.com/viewthread.cfm?qid=416967
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# A coming engineering shortage ? ---- Who agrees ?62
## A coming engineering shortage ? ---- Who agrees ?
(OP)
A recent article says that there will be an acute shortage ... particularly in the electrical field !!!
http://www.csemag.com/single-article/the-coming-en...
Who agrees ???
Who strongly disagrees ???
MJCronin
Sr. Process Engineer
### RE: A coming engineering shortage ? ---- Who agrees ?
"Strongly disagree" doesn't begin to cover it.
Mike Halloran
Pembroke Pines, FL, USA
### RE: A coming engineering shortage ? ---- Who agrees ?
Maybe in certain fields. Power engineering is seeing a shortage that will only get worse in the next five years. The magnitude of the shortage is grossly over exaggerated though. Salaries are not yet reflecting a true shortage but more years of total experience in each department is dropping as people leaving due to retiring are being replaced with fresh grads.
### RE: A coming engineering shortage ? ---- Who agrees ?
I probably don't have a great "feel" for the engineering field as a whole, but I would guess the future will be something like this:
People with engineering degrees: No shortage
Experienced engineers with deep and confident knowledge of their field: Few and far between
As a young engineer working for a small town manufacturer, I'm not sure I'll ever make it to the second category.
### RE: A coming engineering shortage ? ---- Who agrees ?
I agree with the part that I read. And I agree that my salary is not sky rocketing. And I am looking forward to retirement.
There is a shortage of power engineers, and schools teaching electrical power.
I'm not sure this applies to mechanical engineers, as so few of us know what you do.
### RE: A coming engineering shortage ? ---- Who agrees ?
That's talking about a VERY narrow segment of EEs, even. There may actually be a bit of a shortfall because colleges haven't really been emphasizing power engineering as a viable sub-discipline, but they hadn't been doing that since I was in college, which was 37 yrs ago, so if there were a shortage, it should have already been evident by now.
The big issue is the 25% over 55 bit. Given the state of most people's retirement savings, it's highly likely that most of these people won't retire unless they can get Social Security maxed out, which would be at 66+, which is more than 12 yrs away for the youngest of that group, and that age is expected to shift further out to 67+ for those born after 1960. And these people would have never all left at the same time.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers
### RE: A coming engineering shortage ? ---- Who agrees ?
7
If there is any shortage, it is a shortage of the time companies allowing senior engineers to mentor junior or new-hire engineers.
### RE: A coming engineering shortage ? ---- Who agrees ?
3
This kind of article comes out every time when something (or somebody?) threatens H-1B visas.
"For every expert there is an equal and opposite expert"
Arthur C. Clarke Profiles of the future
### RE: A coming engineering shortage ? ---- Who agrees ?
Yawn.
We see these dire warnings continuously- even during recessions. The shortage is seldom claimed to be current- it's usually just around the corner. Soon enough to be worrisome, but far enough away that current measurements of employment levels, wages etc. are deemed to be irrelevant to the discussion about whether or not it's a real problem. Sometimes, it's a current shortage of mid-level people in some cyclic industry which completely stops hiring young people during every down-turn in the economy, which is then generalized to the entire engineering profession... For instance, I can predict with 100% certainty that the oil and gas industry will be screaming "shortage" the next time oil prices rise. All the people they're laying off right now, and the tens of thousands they laid off this past year, will have moved on to other things, retired, or be so far from their oil and gas past that they wouldn't be considered eligible for re-employment.
It has been happening like this for at least sixty years.
Google "IEEE Spectrum STEM crisis is a myth" and read that paper. He does the research and shows the pattern.
### RE: A coming engineering shortage ? ---- Who agrees ?
I shared this article with two of my EE buddies last night, and they both said their companies reflect these assertions perfectly. One is a project manager for a utility, and the other designs substations at a large engineering firm. Both reported very large age gaps among power engineers. One was already aware of and educated on the issue. He believes the gap is due to the more fun and interesting choices EE's have had for the past few decades. e.g. designing computers and high tech gadgets. Power engineering has been boring and uninspiring by comparison. However, that is changing now that more cutting edge technology is coming to the power industry all the time.
### RE: A coming engineering shortage ? ---- Who agrees ?
Comocokid,
Why devote time to training when we are already behind schedule, over budget, and understaffed? ;)
FoxRox,
Not much is changing in the power industry as people make it out to be. There really is not that much that is "cutting edge" at least in comparison to other industries. No one is going to magically figure out a better way to transmit power over transmission lines. Yeah, super conductors are being used or proposed but those are for odd applications like where space is an issue in NYC or for a super substation like Tres Amigas that will connect the Eastern,Western, and Ercot interconnects together to allow wind generation in the midwest flow more freely. Bus protocols like 61850 will change how the substations wired, and tested but the general relay protection philosophies will very likely be the same. Protection philosophies have not changed much even in the move from mechanical to electronic relays. Power electronic devices are used but in very limited applications. The biggest change that I see is the amount and type of green energy being connected to the grid. A lot of upgrades and changes will also need to be made when electrical cars become prevalent. Depending on how slowly the car charges, it will increase the household kwh draw by mutiple, I think in the 2-5 range, during charging.
Compliance to NERC regulation is becoming a cottage industry in of itself. I don't know. I like it because there are a lot of nooks and crannies and when you pull out 40-100 year old text, almost all that you read is still relevant. With that, experience is always valued as opposed to in the .COM industry where fresh grads sometimes are valued over people who have been in the industry for a long time due to them having experience with whatever the new programming language is. Nobody is putting power engineers with 30+ years of experience out to the pasture. It is a mature industry that in my opinion shouldn't be using something like smart grid (too often a solution without a problem) to convince fresh grads that the field is becoming "livelier". It should be instead sold on the merits of being a mature industry with an old and huge 100 year knowledge base that is all still relevant and will never become obsolete.
### RE: A coming engineering shortage ? ---- Who agrees ?
2
I can't tell you how many sleepless nights I've suffered through.
Check out Eng-Tips Forum's Policies here:
FAQ731-376: Eng-Tips.com Forum Policies
### RE: A coming engineering shortage ? ---- Who agrees ?
2
I do a lot of the intern hiring for my department and find that about 1/2 of the students I interview don't want to be engineers in the long run so they don't put in the effort to pay their dues to become good engineers early in their careers.
no shortage of engineers, not many stick with it
### RE: A coming engineering shortage ? ---- Who agrees ?
truckandbus: only 30% of engineering grads in Canada work as engineers, so that 1/2 of the students you interview who don't want to be engineers are in good company.
However, your anecdotal observation of the students you interview runs contrary to the measurements. Our local engineering regulator PEO has been surveying substantial numbers of 4th year engineering students each year for quite a few years, and the results are consistent: over 90% of the graduates will either definitely or probably seek a career in engineering. Only about 6-10% know in 4th year that they are going to pursue something else, i.e. medicine, law etc. So that leaves about 60% of the graduating class, ending up doing something else by default, not by choice. And after a few years out of engineering, they're considered "spoiled" and not suitable for re-use. They've lost their profession for good.
Why do so many fail to gain entrance to the profession? Too few employers are willing to take them on and train them. They expect to find people with 10 yrs of relevant experience gained elsewhere, who can hit the ground running. That only works a) during recessions or b) if you offer significant salary premium. People who build their businesses on that kind of growth model SHOULD find themselves with a shortage of candidates in my opinion- they're shortchanging not only themselves, but the whole profession.
### RE: A coming engineering shortage ? ---- Who agrees ?
I suspect any shortage would be in quality, not quantity. Employers, regulatory, and boards can always lower the bar to address demand.
I used to count sand. Now I don't count at all.
### RE: A coming engineering shortage ? ---- Who agrees ?
The Raising the Bar initiative is raising bar. A masters degree will basically be required to obtain a PE soon.
### RE: A coming engineering shortage ? ---- Who agrees ?
I think there may be a shortage looming, and the retirement boom is only one factor. In the case of the US power industry, there is a rapid change occurring that will require an increase in the number of electric power engineers to address. Intermittent renewable energy sources, large scale storage batteries, smart meters and demand management impact, and modernization of the grid to bring it to international standards cannot be accomplished simply by snapping one's fingers. I think the response of the colleges should be to aler their curriculum to better address these upcoming issues and back off on training students for legacy technology that is slowly but surely becoming irrelevant.
"...when logic, and proportion, have fallen, sloppy dead..." Grace Slick
### RE: A coming engineering shortage ? ---- Who agrees ?
@moltenmetal - what I am finding is that the new grads want to start in engineering but don't want to end up as the seasoned, grey-haired go-to person with 20 years in the trenches.
### RE: A coming engineering shortage ? ---- Who agrees ?
I think the comment on quality is a good one, as many companies believe they can hire consultants when they need help. However, I have seen a lack of quality from such consultant groups, and employees that jump from company to company.
Electric utilities have been hiring EE's without power background as a way to keep up with the need. This requires companies to do internal training on the power system.
The attraction of the utility industry is stability, so we see more people tired of the high tech job jumping. However, the background in high tech typically does not translate well.
It is true that many companies don't do much training, and some of that is a management problem, but smaller companies can't justify the staffing to train new people (Utility commissions pressure companies to keep staff low). But the NERC pressure is requiring more engineers with understanding of the issues, as well as staffing of regional groups, and new industries entering the power field.
### RE: A coming engineering shortage ? ---- Who agrees ?
truckandbus: you mean the smarter kids are waking up and smelling the cat food? Moving to gigs which give them more reward for less effort and risk? The little rascals- how dare they?
There's some attrition out of the profession to SNORGY's favourite MBA route, for sure. That shows up in the numbers- a somewhat larger % of eng grads are employed as engineers 0-10 yrs post grad than in the upper years of experience. Some of that attrition though occurs when people are let go from a cyclic industry and not picked up as engineers thereafter- that too happens.
### RE: A coming engineering shortage ? ---- Who agrees ?
3
Based on my own experience the ones who migrate to the MBA programs tend to be the least competent. I worked directly for one of these imbeciles several years ago, and he couldn't engineer his way out of a paper bag. He ended up being a VP and got to make the call on engineering decisions. It was ugly...
Maui
### RE: A coming engineering shortage ? ---- Who agrees ?
Maui,
It proves the old saying" the people with a B average work for the government, and the people with the A average work for the people with a C average".
"...when logic, and proportion, have fallen, sloppy dead..." Grace Slick
### RE: A coming engineering shortage ? ---- Who agrees ?
2
Can't be a shortage of employees, only a shortage of willingness to pay more.
### RE: A coming engineering shortage ? ---- Who agrees ?
Dave, I'd never heard that before, but it sounds about right.
### RE: A coming engineering shortage ? ---- Who agrees ?
OK, you're right- I forgot to put "smarter" in quotation marks...what I meant is the ones who leave for greener pastures by choice a) aren't so in love with engineering that they see it as an avocation rather than merely something they do for money (you're right- often, that's because they aren't all that good at it), and b) they're the ones who wake up and realize that engineering, especially as an employee, isn't nearly as good a gig as it was thirty years ago, and if you really want to earn some money you've got to find another way to do it. Median pay in Ontario for an experienced (level D) engineer is now on par with the median pay of teachers in the province.
### RE: A coming engineering shortage ? ---- Who agrees ?
Wow. Moltenmetal that salary statistic is brutal. No wonder engineering grads are jumping ship. With wages that low less technical low pressure jobs with similar pay will always win over all but the most dedicated, unless pay dramatically increases with experience.
### RE: A coming engineering shortage ? ---- Who agrees ?
moltenmetal,
Teachers in Ontario are reasonably well paid, although engineers don't get the summer off.
Anatomy of an Ontario teacher’s paycheque .
Remember of course, that these are Canadian dollars.
--
JHG
### RE: A coming engineering shortage ? ---- Who agrees ?
6
I've heard this one before.....and at the bottom of it is typically a shortage of cheap engineers.
### RE: A coming engineering shortage ? ---- Who agrees ?
My argument isn't that teachers are overpaid here- I think they earn fair compensation, particularly when they (inevitably) reach the top end of the pay scale. BTW, the top end of the payscale IS the median now, because more than 1/2 of the teachers in Ontario have achieved the top of the payscale. They don't retire, even when they can and should- my son received more instructional hours in gr 6 from a 70 yr old "retired" principal who was "double dipping" as a long term occasional teacher (long term substitute). He's obviously been doing this for a long time, and getting away with it as a result of the collective bargaining agreement, while gifted young teachers like my niece just starting out cannot get a board position and languish on the LTO list for YEARS...
My question is simply this: IF we feel as a society that a teacher is worth their (equivalent of, once holidays are compensated for) $100,000 CDN/yr PLUS excellent benefits (the best defined benefit pension plan in the country- even federal employees don't have it that good!), is a similarly experienced engineer not worth more than that? The market at the moment says "no", as evident from the salaries of engineers relative to teachers, but ONLY because teachers are unionized and engineers for the most part are not. ### RE: A coming engineering shortage ? ---- Who agrees ? I think there will be time when many extra field will come into picture and engg would get any importance. No jobs for engg have to do some extra and try for many more extra degrees... Sanika Patel http://crbtech.in/CAD-CAM-Training/ ### RE: A coming engineering shortage ? ---- Who agrees ? I propose that if the US imports enough engineers, that the quality of engineers in other parts of the world will decrease. The same with doctors, and taxi drivers. So from that a point of view, it might be better for us to import as many engineers as possible. I also propose that there will be enough engineering grads that just can't cut it, and will become teachers. ### RE: A coming engineering shortage ? ---- Who agrees ? https://dazeinfo.com/2014/10/28/1-5-million-engine... http://www.thenewsminute.com/lives/609 And there are tons of articles about industry screaming how inadequate fresh graduates and that is why they hire only a small fraction: http://timesofindia.indiatimes.com/city/mumbai/Onl... http://www.wsj.com/articles/SB10001424052748703515... Same stuff as in the states. Fresh grads suck. Nevermind that they need training. Only a fraction of fresh grads go into engineering. Wages are stagnate despite industry's cry that there is a shortage. I am not really convinced the quality anywhere is affected that much by workers leaving to work abroad. The glut is too large for quality or wages to be affected much by people leaving the country in my opinion. ### RE: A coming engineering shortage ? ---- Who agrees ? Should hardly be surprising; every developing country is attempting to corner the world's markets in engineered goods, but it also requires very cheap labor, so all the more reason to pump up the supply to bring the labor costs down. TTFN (ta ta for now) I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers ### RE: A coming engineering shortage ? ---- Who agrees ? I believe it is part of the over all trend to reduce labor costs by bring in more supply of labor. That I don't disagree. But there also seems to be a shortage of quality power engineers. And Tech.'s, and Linemen, and truck drivers. For that matter, there is a shortage of quality people available. ### RE: A coming engineering shortage ? ---- Who agrees ? "For that matter, there is a shortage of quality people available." That's because they're already gainfully employed. The big question is whether we're at the point where any further increases in supply of quality people will drastically drop labor rates, because not every job requires the "best" candidate. Someone who is "good enough" will undercut the salary rates. In some respects, all this emphasis on driving people into STEM is a lot like an external market manipulation, which we all know has potentially deleterious consequences. TTFN (ta ta for now) I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers ### RE: A coming engineering shortage ? ---- Who agrees ? #### Quote (cranky108) I propose that if the US imports enough engineers, that the quality of engineers in other parts of the world will decrease. Don't you think that if US will import cheap engineers, the quality of engineers in other parts of the world will actually increase? "For every expert there is an equal and opposite expert" Arthur C. Clarke Profiles of the future ### RE: A coming engineering shortage ? ---- Who agrees ? I have 20 plus engineering work experience to senior,principal and manager level. My view is that there is no shortage of engineers and will never be mainly to do with globalization and mass migration. In fact, I am well aware of universities in various countries closing down or consolidating departments as are not able to recruit engineering candidates. ### RE: A coming engineering shortage ? ---- Who agrees ? The UK is seeing a similar problem in the heavy electrical industries - power generation, transmission, primary distribution and the process industries such as petrochemicals and... well, once I could have included mining, steel, and the like. Not now, not today. There is an entire generation which is under-represented in power engineering - the one I'm part of. It's the 30-year harvest from the seeds sown during the privatisation (read: decimation) of the state-owned utilities in the 1980's and the recession of the late 80's and early 90's. Recruitment and training pretty much stopped for two decades before the power industry started to wake up and realise that a serious problem was developing, with the result that my generation is largely missing from an industry still dominated by the 'grey haired guys' who survived the huge cull. During that period many universities closed their unpopular power engineering classes because they were (rightly) seen by students as difficult, old-fashioned, and with lousy employment prospects, while the universities saw them as space-hungry, capital-intensive, minority-interest subjects. Today a handful of universities have re-established first-rate power engineering schools and there are some really bright prospects coming out of these universities who will be excellent engineers once they gain industry experience, but they can't pick up two or three decades worth of experience overnight, and the old-timers are retiring faster than these new folks are gaining experience. I see this going on for another decade, maybe fifteen years or so until some sort of balance between supply and demand is restored. At that point I'll be getting worried that some of these new grads will be a lot better at this stuff than I am. ### RE: A coming engineering shortage ? ---- Who agrees ? ScottyUK. Whilst the situation regarding engineers may be improving in the UK these new graduates will be entering an industry where the critical path for distribution projects is dictated by the availability of cable jointers. The bigger skills shortage in my opinion is of craftsmen in trades which most people do not even know exist. ### RE: A coming engineering shortage ? ---- Who agrees ? I guess we are lucky in those respects, because we have a resource of people retiring from the military, and who are willing to be trained in additional skills. Truck driving skills is not a problem. It's the power engineers, INC tech's and relay tech's we have difficulty finding. ### RE: A coming engineering shortage ? ---- Who agrees ? Actually cranky108, I keep hearing about shortages of truck drivers - even a few years ago when unemployment was high. Seems to be mostly that the pay isn't that good, especially given the long hours away from 'home' for long distance drivers etc. Plus all the 'self employed' shenanigans of making the drivers own their rigs but be treated like employees in most ways... Posting guidelines FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm? (probably not aimed specifically at you) What is Engineering anyway: FAQ1088-1484: In layman terms, what is "engineering"? ### RE: A coming engineering shortage ? ---- Who agrees ? Shortages of long haul truck drivers. Have you heard of shortages of local truck drivers? I suspect some trucking companies do play games with employees. My comment was about the skills not the people willing to do the job. Besides utility trucks, in general, are not that big. We do have special people for driving oil rigs, and other larger things. But in general the line trucks have to be able to go over city streets, and dirt roads. ### RE: A coming engineering shortage ? ---- Who agrees ? Andybro, Yes, I agree there are chronic shortages of jointers, also protection engineers, TP141 commissioning techs... the list goes on. Managers are ten-a-penny though! ### RE: A coming engineering shortage ? ---- Who agrees ? There is some truth there. "You get what you pay for" is really true. If you are hiring truck drivers at minimum wage, you are likely to have shortages. Paying engineers more will increase the pool of engineers, but it will take time to train them, and weed out the bad ones. So from that perspective, there should be no shortage of engineers. Just a shortage of companies who are willing to pay a reasonable rate. Which brings to mind how so many companies are not willing to pay their in housh engineers more, but are willing to hire consultants at three times the rate, for second class work. ### RE: A coming engineering shortage ? ---- Who agrees ? "there should be no <long term> shortage of engineers <with the required expertise>. Just a shortage of companies who are willing to pay a reasonable rate." You may be onto something there. Posting guidelines FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm? (probably not aimed specifically at you) What is Engineering anyway: FAQ1088-1484: In layman terms, what is "engineering"? ### RE: A coming engineering shortage ? ---- Who agrees ? #### Quote (cranky) Which brings to mind how so many companies are not willing to pay their in housh engineers more, but are willing to hire consultants at three times the rate, for second class work. Given the overhead multipliers in most large companies, paying only 3 times as much money for work which is only 2nd class would be seen as excellent value for money! ### RE: A coming engineering shortage ? ---- Who agrees ? The fact that consulting engineers are available means that you don't have to continue to feed an expensive, in-house, qualified engineer. At a 3x multiple, that's still probably less than double the net cost per hour for an in-house engineer, and so long as you need the consultant less than 6 months per year, you're ahead Having an in-house engineer means more than just the sheer cost, you have to feed that one guy stuff that he's interested in doing, and if you don't do that, at best, the guy gets rusty over time, and at worst, he bails after a couple of yrs of fixing stupid crap that the cheap engineer should be able to fix, but can't. This also means that your cost to maintain in-house capability goes up even further if you have to pay for acquisition of the next qualified engineer, in head-hunter fees, advertising, and down time to interview candidates. There are certain disciplines that we've been completely unable to fill because of the reasons above. TTFN (ta ta for now) I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm ### RE: A coming engineering shortage ? ---- Who agrees ? 2 A 3x multiplier on salary is probably low on an employee of a large company burdened with lots of MBAs, VPs, PIPs, HR and other alphabet soup folks... ### RE: A coming engineering shortage ? ---- Who agrees ? hmm. We only use a 2x multiplier. ### RE: A coming engineering shortage ? ---- Who agrees ? The lower you pay your engineers, the higher the multiplier has to be. Generally. ### RE: A coming engineering shortage ? ---- Who agrees ? Generally, smaller companies tend to have lower multipliers. A significant portion of our multiplier pays for facilities that smaller companies might not have, such as security officers, SCIFs, gobs of lab equipment, etc. 8% of our personnel are associated with security and IT. While IT does the usual PC problems, they also are constantly keeping the PCs updated and virus scanned. Every single classified computer has to be audited on a routine basis by IT. Even then, we are all still pretty highly paid, although not as well paid as what Facebook and Google interns are supposedly being paid this year (~8k/month) TTFN (ta ta for now) I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm ### RE: A coming engineering shortage ? ---- Who agrees ? The topic of this thread has drifted to a related, but interesting one. Labor rate multipliers are a useful tool for establishing a profitable price to charge for small routine jobs or orders. These multipliers are very frequently misused by middle management and bean counters to show large cost savings by reducing head count. Reducing head count of those to whom the multiplier applies, does not reduce overhead and simply increases the multiplier for next year when a new multiplier is calculated. This leads to what I have called the "corporate death spiral", where companies price themselves out of business by constantly increasing the multiplier. The only way to decrease the multiplier is to increase sales and therefore headcount. ### RE: A coming engineering shortage ? ---- Who agrees ? My favorite sign over an engineer's desk: "Note to management: You are overhead; I am profit" ### RE: A coming engineering shortage ? ---- Who agrees ? I think in a nutshell, the engineering profession as a whole is shrinking in the western world while increasing in the developing countries due to a host of political and economic reasons, on the same token the number of professionals engaged changes accordingly. ( my view is that many engineers slip out of the profession as they mature, after 10 -15 years on average. On the opposite side there seems to be an inverse correlation with the number of accountants and lawyers getting into the market. On multipliers; we charge junior staff at a higher x, than the senior one. ### RE: A coming engineering shortage ? ---- Who agrees ? IRStuff, 8k a month in San Francisco is like 4-5k a on a month in a lot of other places. If you look up BART salaries, there are plenty of "uneducated" people breaking 100k. I have a relative that worked closely with CEO Marissa Mayer at Yahoo and he still needed a lot of help from his parents to buy a house. ### RE: A coming engineering shortage ? ---- Who agrees ? Silicon Valley has been consistently expensive over the last 30+ years. When I was shopping for a house in 1982, a ramshackle "house" in the hills above Los Gatos that appeared to be patchworked with various colored corrugated sheet metal was listed at$130K; the road was an unpaved single lane, and it looks so bad I didn't even bother to look inside the house. I wound up buying a 1600 sq. ft. tract house for $138k, and that required parental help as well. That same house is guesstimated by Zillow to be$1.25M today. The main difference is that the multiple of salary went from about 4:1 to 10:1
But, bear in mind that the $8k for the intern is in ADDITION to: > free housing, but shared with a couple of other interns > 3 meals a day during work week > free transpo to/from work to the free housing For a junior in college, that's a exceptionally sweet deal, and, that's increased from 3 years ago when the intern salary was$6k/month.
TTFN (ta ta for now)
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### RE: A coming engineering shortage ? ---- Who agrees ?
Does anyone have any evidence or links to research that counters the "hype" that there is an engineer shortage? I don't believe there is either, but you'd think someone had actually looked into it and published research, even if it's just a magazine article.
### RE: A coming engineering shortage ? ---- Who agrees ?
I've posted these before, but I never get tired of posting them again:
A detailed, well-documented study of the engineering labour market in Canada, in Ontario in particular, based on solid census data and other similar sources:
The conclusions, in brief:
- only 31% of engineering grads in Canada work as engineers or engineering managers. It is the lowest match rate between education and work placement of any of the country's regulated professions
- the lines of the number of engineering grads (supply) and the number of engineering jobs (demand) have different slopes, and have diverged steadily over the past two decades
- a larger fraction (33%) of engineering grads work in jobs not requiring a university degree of any kind. That alone is clear evidence of a massive under-employment situation for engineering grads in Canada
- the 69% working outside engineering, earn on average 20% less than the 31% who do, so if they've left the profession voluntarily they've done so against their economic interests
- 92% of engineering 4th yr students surveyed indicated that they definitely or probably will pursue a career in engineering- obviously, many fresh grads are unable to find work and hence lose their chosen profession rather than choosing to abandon engineering
Another well documented study, indicating a systemic pattern of predictions of future STEM shortages that has happened since the 1940s:
http://www.theatlantic.com/education/archive/2014/...
http://spectrum.ieee.org/at-work/education/the-ste...
### RE: A coming engineering shortage ? ---- Who agrees ?
The STEM program here was such a failure that they had to add "arts" and make it STEAM. This was to entice at least someone, even artists, to go into engineering.
### RE: A coming engineering shortage ? ---- Who agrees ?
I guess it is kept silent. Although doing ok at math and science, my kids have no desire to go STEM either. So be it.
### RE: A coming engineering shortage ? ---- Who agrees ?
I would take STEAM if it brought back the impression that engineering is or can be a creative endeavor. Sometimes, I feel like the public thinks that engineering is a souless endeavor like bookkeeping.
### RE: A coming engineering shortage ? ---- Who agrees ?
Well, I saw the recent movie "the accountant", and I had previously thought the accountants job was pretty dull, but Affleck ( the accountant) must have killed 200 people within 1 week of dull work. Maybe they should make a movie called "the engineer" with similar blood and guts to draw more kids to STEM..
"...when logic, and proportion, have fallen, sloppy dead..." Grace Slick
### RE: A coming engineering shortage ? ---- Who agrees ?
"...when logic, and proportion, have fallen sloppy dead..." Grace Slick
FTFY
### RE: A coming engineering shortage ? ---- Who agrees ?
2
Engineering seems to be one of the most difficult white collar ways of making money.
High responsibility
High Stress
High visibility
Low / Slow upward movement
Low respect
Med pay
I'm really getting tired of it. I'm pretty much ready to move on. Maybe I'm a 'B' engineer, but I feel like there is only one person on our engineering team better than myself. Who knows. I'm tired of fighting all the time, tired of every team pushing me to make 'easier' decisions for mfg, cost and time. Tired of building Bill of Materials. Tired of B / C engineers asking me simple problem solving questions. And I hate how software knowledge is more important than knowledge. Some person knows how to run CFD and Ansys and his resume is gold. Same guy doesn't know what to do when the customer asks him about clearances without running a stupid 3D software. Why didn't engineers divorce themselves from 3D software? Just contract it out. I don't care how to make the grid to do this or do that. I need to know what the stress is here. Make it happen.
I guess you can tell that I'm over the whole thing.
: )
### RE: A coming engineering shortage ? ---- Who agrees ?
I have to agree with most of the above ! Since globalization and the rise of industralization in the far east, and the shift to service industries in the west, the future of engineering opportunities as we know it, is limited.
### RE: A coming engineering shortage ? ---- Who agrees ?
Unless you innovate. I realise that the opportunity for innovation is limited in 'design to code' industries, but believe it or not somebody did once get moment plasticity design of steel frames onto the books, so it is possible.
As to pay, clerical engineering is not well paid. Neither is clerical banking.
Cheers
Greg Locock
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### RE: A coming engineering shortage ? ---- Who agrees ?
Where I work is chock full of foreign citizens on visas. Management there must be claiming an engineer shortage so they can reach out to these foreign workers and pay them MUCH less than a US citizen.
Tunalover
### RE: A coming engineering shortage ? ---- Who agrees ?
3
STEAM is a meaningless term. It's an attempt to lump "arts" in with science/technology, engineering and math just to give "arts" some cachet, rather than trying to imply that there is "art" or creativity in any of those other subjects.
What- languages aren't important? Or the social sciences? Or economics?
There is no STEM shortage nor any shortage of kids interested in pursuing STEM careers. There is a persistent shortage of employers willing to take on fresh graduates and train them. That shortage results in a shortage of people at the putative "peak" return on investment for an employer, i.e. someone with ten- not two or thirty- years of relevant experience gained at someone else's expense. These employees will be in perpetual short supply if employers don't realize that professionals need to be built from good raw materials, not purchased like widgets off a shelf.
awhicker84: I hear you. I get tired of people telling me what a good gig engineering is. The risk and stress to reward ratio for the average engineer is terrible. We have allowed our profession to be commodified, primarily by selling our services by the hour rather than getting paid for the value we create by embodying our engineering in products which we sell. When all you sell is man-hours, all engineers are reduced to equivalent billing units and subject to hourly price competition, tempting employers to stuff cubicles with billing units of questionable virtue in order to get ahead. We find it's far easier to be compensated in accordance with the value we create if we forget about selling man-hours and instead make a product which embodies our engineering and sell that. It's also a hell of a lot more rewarding.
### RE: A coming engineering shortage ? ---- Who agrees ?
It's the engineering shortage that allows me to say 'NO' rather than having to kill butt to keep my job. I like that.
### RE: A coming engineering shortage ? ---- Who agrees ?
Lawyers sell man-hours too, but as a profession they were smart enough to set up a closed shop and then charge premium rate for their services. Their business model works for them, while ours doesn't.
### RE: A coming engineering shortage ? ---- Who agrees ?
WE engineers only control the design. We don't maintain control product marketing and sales.
Reaction to change doesn't stop it
### RE: A coming engineering shortage ? ---- Who agrees ?
Here in Ontario, the other thing that distinguishes law and medicine from the rest of the regulated professions is that in each case, 80-90% of their licensees are also members of their advocacy body. In the case of doctors here, their advocacy body is basically a union- it negotiates fees from our single payor medical insurance system, i.e. the provincial government.
We engineers instead went the other way- we were licensed for eighty years before we founded an advocacy body, used the excuse of not having one to not do ANY advocacy on behalf of professional engineers because doing so would be somehow a conflict of interest...and eroded our own restricted realms of practice by permitting an industrial exemption from licensure and a Certificate of Authorization program to permit corporations to do professional engineering in their own name (i.e. what can amount to one signatory engineer taking responsibility for the work, with a crowd of non-engineers doing the actual work).
The median salary for a level D engineer is the same as that for a teacher here in the province, once you account for all the extra vacation the teachers get. And we're not done our race to the bottom yet- we keep on digging...
### RE: A coming engineering shortage ? ---- Who agrees ?
"eroded our own restricted realms of practice by permitting an industrial exemption"
And yet, in California, where there is an industrial exemption, engineers at Alphabet got high 6-figure salaries and most engineers in Silicon Valley do very well. This argument continues to come up, yet, for someone like me, who NEVER sees the public, NEVER works on anything that impinges on public safety, there's this harping to get licensure. But for what? Ultimately, we still get sold by the pound, because that's the way contracts are set up. But, my pay is fine as is the pay of all the engineers in the company, so what rationale is there for licensure?
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
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### RE: A coming engineering shortage ? ---- Who agrees ?
Maybe, they were talking about running into a shortage of engineers to import. ;)
### RE: A coming engineering shortage ? ---- Who agrees ?
In US the engineering workforce is not swamped by "foreign engineers" as legal migration is way more regulated than in Canada, Australia, New Zealand. In US without a "legal " migration you cannot get a professional job.
### RE: A coming engineering shortage ? ---- Who agrees ?
Not exactly. Legal migration is way more regulated yes, true, but that doesn't help when the supply was legally flooded.
Reaction to change doesn't stop it
### RE: A coming engineering shortage ? ---- Who agrees ?
What exactly is a " high 6-figure salary"? We should also account for cost of living in differing areas.
### RE: A coming engineering shortage ? ---- Who agrees ?
Let's say that it was "high" enough that more than a few have since become semi-retired, just from banking their salaries. Alphabet supposedly experienced a severe "brain drain" in their self-driving car group because of this.
For "ordinary" mortals, internships last year were priced at effectively $96 k/annum; this was for college students still in school. Starting salaries were probably on the order of$120 k.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
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### RE: A coming engineering shortage ? ---- Who agrees ?
Not sure if is correct to lump together the software engineers with the physical science type engineers in your comparison. Some are still reluctant to call software engineers, engineers. The difference is more than semantics.
### RE: A coming engineering shortage ? ---- Who agrees ?
2
IRstuff: a diminishingly small number of engineers earn those high salaries. Yes, a few engineers in Canada earn high salaries too- some of them actually still do engineering...You keep bringing up the salaries of engineers working for places like Google as if it actually indicates some kind of trend meaningful to the engineering profession at large, and it simply doesn't.
My point is simply this: engineers here in Ontario, within living memory, earned more than either doctors and lawyers. We now earn a fraction of what those professions earn in median terms- in fact we're now on par with teachers in terms of pay. It's very clear WHY that reversal happened here- we allowed our profession to become a commodity, whereas the other professions didn't. Teachers unionized- so did the doctors, though they don't call their union a union. Lawyers didn't unionize, but they didn't allow law firms to practice law in their own name- they permit partnerships but don't grant licenses to corporations to practice law in their own names using armies of paralegals, for instance. There is no exemption from licensure for the practice of law, period- lawyers are very good at making rules which ensure there is always a job for lawyers. They also are still the most prominent profession in politics.
### RE: A coming engineering shortage ? ---- Who agrees ?
The notion that is salaries would increase due to licensure is flawed. If there were 10 times the number of licensed engineers, the salary structure would collapse altogether, simply because there would be an over supply.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
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### RE: A coming engineering shortage ? ---- Who agrees ?
Salaries won't increase again. No point in closing the barn door 30 years after it was kicked open- that horse is dead. So you're right- even if we were to get rid of the industrial exemption and reform the C of A, the market is so flooded with licensees that wages would not rise in a meaningful way. The likelihood of meaningful reform to the C of A is zero, and even the IE in Ontario- the only province which has one- can't be removed without a hue and cry from the business lobby- we tried two or three years ago and failed.
Right now even the requirement for 1 yr of experience mentored by a licencee prior to licensure (so the licensee at least has a chance to determine if the person actually understands the legal and ethical requirements of licensure) is under attack as contrary to the human rights of immigrant engineers. So the trend is for even more supply. The prospects for a demand-side solution to falling engineering wages are basically zero. With the profession only able to "capture" less than half of its own graduates, it's tough to see how things could get worse, but we're trying our best. I'm sure if we maintain a sufficiently positive attitude about what a great gig it is to be an engineer, and how there are always shortages of engineers, and how well engineers are paid, we'll be successful.
### RE: A coming engineering shortage ? ---- Who agrees ?
#### Quote:
The notion that is salaries would increase due to licensure is flawed. If there were 10 times the number of licensed engineers, the salary structure would collapse altogether, simply because there would be an over supply.
Agreed. One approach that has been suggested however is a Grad degree as a minimum for licensure. I've never agreed with the idea, but I guess it actually would cut down on the supply.
### RE: A coming engineering shortage ? ---- Who agrees ?
Will it be a shortage of engineers? Or will it be a shortage of talent?
Companies sometimes will assign a young engineer primarily with repetitive and dull responsibilities that don't grow their skillset. Once you kill a guy's enthusiasm, it won't come back as strongly ever again. Throw the young guys in the mix enough to keep them engaged and challenged.
"Formal education is a weapon, whose effect depends on who holds it in his hands and at whom it is aimed." ~ Joseph Stalin
### RE: A coming engineering shortage ? ---- Who agrees ?
"With the profession only able to "capture" less than half of its own graduates,"
THIS pretty much tells you that we're in an over supply condition that's unlikely to change. While a graduate degree could potentially drive down the supply, I doubt that there will be much impact. In my high school years, taking 3 AP classes was considered to be high achieving, and there was no IB whatsoever. Today's high schoolers, in the college prep pathway, take at least 12 AP classes, and many take an additional 7 IB exams. With an appropriate selection of such classes, and a firm and early decision of a major, finishing college in 3 years is achievable, so adding another year for an MS simply brings you back to 4 years of college, total.
Earlier there was a comment about CS not being engineering; UC Berkeley's College of Engineering's CS degree is EE-CS (they call it "eeks"), i.e., electrical engineering/computer science, so for them, CS is an engineering degree and discipline, and graduates have to fulfill the requirements of an engineering degree.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
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### RE: A coming engineering shortage ? ---- Who agrees ?
3
If you make masters degree a requirement then you'll just end up with Academia getting rich and an increase in student debt etc.
It's one thing to raise the bar because you actually need the extra skills etc. you get from a Masters, using it to crudely prune the supply side is very questionable in my view.
One aspect to the 'shortage' that I saw alluded to in an article a while back is that some very capable students in STEM perceive that it's harder for them to keep their grades up than their colleagues in some other subjects so they transfer. I forget if they followed this as far as checking that with these other degrees they get similar employment opportunities & ROI etc. One might argue this could be a good thing that the people staying in STEM are more engaged & enthusiastic etc. even if not always as academically gifted. Or, one might be concerned that many of the 'brightest & best' are leaving STEM education for paths they see as giving better reward for investment.
Not to fear though if the 'native' STEM Phd candidates drop out to go basket weaving or work on wall street, we'll fill the Phd programs with imported talent (some of it not particularly exceptional) and skirt the H1B limits because student visas can be transferred to H1B without counting against the quota. Then our vaunted tech industry will have all the indentured servants it can handle.
(Sorry, may be a little grumpy today so take with a pinch of salt as needed.)
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### RE: A coming engineering shortage ? ---- Who agrees ?
Star for Kenat. I couldn't agree more with your first two statements.
### RE: A coming engineering shortage ? ---- Who agrees ?
To put things in perspective with the topic, the article linked by the OP was talking about a very specific situation in the power industry, which does likely have a shortage due to an age-gap.
Engineering as a whole could certainly have a glut while the power industry and other niche fields like programming have a shortage. Lucky for them.
As a Mechanical Engineer (BSME), I certainly feel like this is the case. When I graduated five years ago, I had a gut feeling that the piece of paper I received was a dime a dozen.
That being said, I still think there is a chance for superior talent and work ethic (hoping that I have both in sufficient supply) to prevail over a glut of degree holders. It's interesting to discuss the topic, but as an individual it does no good to blame immigrants, government policies, or our engineering forebears for one's own plight.
At this point I often joke that, if I had it to do over, I would have been a dentist or a dermatologist. Work half the time for ten times the pay. Alas, who can predict what the perfect job would look like in their future self's eyes?
### RE: A coming engineering shortage ? ---- Who agrees ?
"article linked by the OP was talking about a very specific situation in the power industry, which does likely have a shortage due to a hiring an age-gap at some point in the past"
I mean, it's not like the ageing process and typical retirement ages etc. are so unpredictable that it's a meaningful excuse.
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### RE: A coming engineering shortage ? ---- Who agrees ?
KENAT, true enough. If there is a real shortage now, it's because they ignored a slowly developing shortage for decades. Students picking majors cannot be blamed for turning away from a future of perceived boredom and mediocre pay.
### RE: A coming engineering shortage ? ---- Who agrees ?
Even when I went to college, which was MANY moons ago, electric power was a waning discipline, other than electronic power supply design. Slobodan Cuk had just invented his converter topology.
TTFN (ta ta for now)
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### RE: A coming engineering shortage ? ---- Who agrees ?
So power engineering is a cycle like the aircraft industry. The cycle is about 30 years.
That being said, many universities don't teach electric power. That maybe because teaching pays so much less than the actual industry.
I am assuming teaching other areas of engineering pays closer to the industry wages.
The other side of it is for a long time microelectronics engineering has paid so much better than power engineering, likely to the point there were very few people going into the power option.
### RE: A coming engineering shortage ? ---- Who agrees ?
The best instructors for power engineering would be retired power engineers. They have the knowledge and can afford to take the relatively poor pay of an adunct professor.
### RE: A coming engineering shortage ? ---- Who agrees ?
I think some of the lack of growth (wrt salaries) has been the sluggish economy. (That may be something we are forgetting here.) Even in the "recovery" years we've had since 2008, it hasn't been 5-7% years (like we had in the mid-80's). In 2004-2007, I was getting outrageous offers to leave where I was working (same thing in the late 90's).
### RE: A coming engineering shortage ? ---- Who agrees ?
"many universities don't teach electric power."
There's just not that much demand for courses. If there were demand, there'd be professors hired to do the teaching.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
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### RE: A coming engineering shortage ? ---- Who agrees ?
Raising the bar for engineering licensure to a Masters degree would not only be a meaningless way to prune the supply- it would just extend the "credential inflation" problem even further. The BA is the new high school as far as employers are concerned, and that's a huge problem in and of itself. The trouble with credential inflation is that higher education in most countries isn't 100% subsidized. There's only so much education a person can afford, unless their parents are rich. So all you'd be doing is making it even harder for people to move up the economic ladder than it is right now. You'll be sorting people all right, but not necessarily by ability, skill, aptitude or intelligence.
The top 10% of engineers can still thrive. But the notion of a BASc being a meal ticket are long, long gone.
The lack of growth in salaries has occurred over decades, and is relative to other professions subject to the same global economic pressures, the same recessions etc. The slide hasn't happened because of recessions- it has happened because we allowed the supply to swamp the demand. And if we keep up this attitude of limitless opportunity in engineering, I'm confident that we can make matters even worse. Every Dean of Engineering in Canada seems to be positively brimming with that positive attitude.
### RE: A coming engineering shortage ? ---- Who agrees ?
Most of the retired power engineers that I know, are consultants, and not teaching. I think the consultant route pays more than teaching.
So are you saying that boring industries will in the future go wanting for engineers, while exciting industries will be swimming in engineers?
Sounds like some industries will be seeing wage freezes.
### RE: A coming engineering shortage ? ---- Who agrees ?
Depends what turns your crank, cranky! Some stuff I find dull as watching paint dry is fascinating to others, and vice versa.
### RE: A coming engineering shortage ? ---- Who agrees ?
Well Cranky, that's where the whole supply and demand thing should cut in.
The premium for power engineers will be so high that it should eventually lead to increase in supply. The premium for courses in power engineering and people to teach it should likewise grow...
Now it's not the smoothest of systems and hits a lot of bumps and snags along the way but in theory should get us there barring gross negligence/self serving etc. at management and government levels and the like.
So we're probably attached to another object by an inclined plane, wrapped helically around an axis.
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What is Engineering anyway: FAQ1088-1484: In layman terms, what is "engineering"?
### RE: A coming engineering shortage ? ---- Who agrees ?
"So are you saying that boring industries will in the future go wanting for engineers, while exciting industries will be swimming in engineers?"
That's mostly true, even outside of engineering. Why is psychology one of the most popular majors in college when the typical graduate winds up in a $35k/yr job as a social worker? Was that really worth borrowing a quarter million that can't be paid off with that kind of salary? Physics 1 used to be a "weeder" class in my school, because the school knew that the plethora of wannabe physicists wouldn't be able to get jobs at the end of the 4 yrs. Of course, the class was so brutal that my roommate declared for Eng. Lit. at the end of that, and that was in a serious engineering school. But, even at the worst, he only paid a total of about$20k tuition in then-year dollars. Even the worst student could expect a loan to salary ratio of 1:1, while currently, it would be more like 2:1 to 4:1, unless you go to a state school.
TTFN (ta ta for now)
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### RE: A coming engineering shortage ? ---- Who agrees ?
Kenat,
The industry will make due. Over standardization and knowing how to use software has been given more weight than understanding. It will just be more bloated and dumber. Utilities are regulated ,too, so the wages are never tied to demand. Unionized master techs are better off than nonunion engineers.
### RE: A coming engineering shortage ? ---- Who agrees ?
The place I work now seeks for Engineers a lot.Not just Engineers,skilled ones.The demand for Engineers increase in modern world.But do not mix it up with traditional Engineers,now areas like medical engineering,QA Engineering,Testing engineering have evolved and replaced the traditional civil engineers(not that they do not have opportunities)but engineering has modified itself according to the modern era and not still dead and will not be in future.
Medical Engineering
(http://www.dimolanka.com/sectors/sector-overview?s...)
### RE: A coming engineering shortage ? ---- Who agrees ?
I disagree. I read an article, granted it is several years old, where it said STEM graduates number in the 800,000. US colleges produce twice the number of STEM graduates as there are jobs in the field.
### RE: A coming engineering shortage ? ---- Who agrees ?
plazma,I read your article and found it has some interesting findings.However I agree that mining and petroleum engineers have attracted the field a lot.Mainly in Calgary,Canada and Perth,Australia where the resources are found in huge amounts.
Medical Engineering
(http://www.dimolanka.com/sectors/sector-overview?s...)
### RE: A coming engineering shortage ? ---- Who agrees ?
Can't see any problem, people can just log into Eng-Tips and get answers just as is done now
It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)
### RE: A coming engineering shortage ? ---- Who agrees ?
Any engineer should be able to look at that graph and understand in an instant what is really going on.
### RE: A coming engineering shortage ? ---- Who agrees ?
It boils down to a drop in engineering demand as the western world shifted to a services type economy while developing economies boost a strong and ever increasing demand for engineering. The faculties, politicians and still many have not adapted to this change but still chasing the higher wage in the west.
### RE: A coming engineering shortage ? ---- Who agrees ?
Politicians know that the jobs for people with a high school education are going the way of the dodo. Their response is to get everyone to go to university...they don't realize that the economic ground under them has completely shifted and isn't going to shift back merely by giving everyone a degree. That engineers provide essential benefits to society and the economy is not in doubt- but it is a non-sequitur to assume that adding 2-3x the number of engineering grads to the market than the economy could possibly use as engineers will have any net economic benefit, much less an economic benefit worth the investment required in providing this specialist education to people who don't actually need it.
### RE: A coming engineering shortage ? ---- Who agrees ?
"but it is a non-sequitur to assume that adding 2-3x the number of engineering grads to the market than the economy could possibly use as engineers will have any net economic benefit"
Sure, it will. That is the basis of supply-side economics, the "if you build it, people will buy it" theory that's been PROVEN time and again to not work, but because it's derived from political dogma, they continue to spout it ad nauseum. A very casual analysis of wage growth vs. wealth of the top 1% vs. corporate profits shows very clearly who really benefits from supply side economics and it certainly ain't us. Minimum wage in the US in adjusted dollars was growing up until supply-side economics was pushed into the mainstream of American politics, and lo and behold, it has DECREASED 40% since its peak in the 1970s. And yet, the top 1% has seen an order of magnitude increase in wealth over the same time frame. Is that a simple coincidence?
If you ever wanted to see a real-life global-scale conspiracy, this might be it.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
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### RE: A coming engineering shortage ? ---- Who agrees ?
I don't necessarily disagree with @moltenmetal's assessment of Canadian engineering - I think similar happens in the USA. However, if I were to argue it (playing devil's advocate) I would look at the entirety of college graduates and their proportion of relevant employment after graduation.
I think it goes without argument that the overall rates of college graduates is rising overall in my own country (USA) as we continue to pressure everyone to "get a degree, any degree, just get a degree because everyone should" which results in a lot of irrelevant education with their future employment.
### RE: A coming engineering shortage ? ---- Who agrees ?
#### Quote:
Sure, it will. That is the basis of supply-side economics, the "if you build it, people will buy it" theory that's been PROVEN time and again to not work, but because it's derived from political dogma, they continue to spout it ad nauseum. A very casual analysis of wage growth vs. wealth of the top 1% vs. corporate profits shows very clearly who really benefits from supply side economics and it certainly ain't us. Minimum wage in the US in adjusted dollars was growing up until supply-side economics was pushed into the mainstream of American politics, and lo and behold, it has DECREASED 40% since its peak in the 1970s. And yet, the top 1% has seen an order of magnitude increase in wealth over the same time frame. Is that a simple coincidence?
At the risk of taking the thread off course......with respect, that is tying a lot of things together that are not necessarily related. Wage growth doesn't really have much to do with tax policy. That is just redistribution after the fact. You can tax the highest wage earners all you want.....and unless the revenues are redistributed later.....it's meaningless. Wages are a direct result of supply and demand, production being increasingly automated, etc, etc.
As far as supply-side goes......whatever its flaws, it was intended as a response to the collapse of the Keynesian school models that went up in flames in the 1970's. (With the coexistence of high inflation and high employment which supposedly was impossible in the Keynesian school.) It also coincided with the entrepreneur revolution of the 80's. (I.e. a need for incentive as productivity declined in the 70's.) It certainly isn't the cure-all the a lot of right-wingers make it out to be (principally because they mismanage the budget aspect of it: i.e. not accounting for a initial slide in revenues). But you'd be hard pressed to find many economists who want the old tax code back. (Even Jonathan Chait admitted this in his book slamming supply-side.)
### RE: A coming engineering shortage ? ---- Who agrees ?
I wasn't specifically referring to the tax code, per se. I was merely pointing out that wage stagnation for the lower and middle classes seemingly coincides with huge increases in wealth in the upper classes. Nevertheless, tax code changes have seemingly helped the upper classes way more than they ever helped the lower classes.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
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### RE: A coming engineering shortage ? ---- Who agrees ?
And maybe the need for everyone to get a degree is because of the decline in public school education. The universities are taking over the job of the public schools.
Another aspect might be that not all the engineering universities are the same, and some of the degrees are given to people who may not be qualified, or go into management, or both.
And yet some in political office still follow the Keynesian theory.
Yet some of the richest people never finished college.
### RE: A coming engineering shortage ? ---- Who agrees ?
#### Quote:
I wasn't specifically referring to the tax code, per se. I was merely pointing out that wage stagnation for the lower and middle classes seemingly coincides with huge increases in wealth in the upper classes. Nevertheless, tax code changes have seemingly helped the upper classes way more than they ever helped the lower classes.
I don't know that the two are connected. The idea that is being hinted at here is that if taxes were higher that would mean more for other classes. (I.e. that somehow employers would give their employees more (presumably to avoid taxation).) And that just isn't the case.
That is, unless the money was redistributed after the fact. On that note, in the era of super high marginal rates (70-90% +) that isn't what happened with revenues anyway (i.e. income redistribution in the form of benefits such as heath care). Defense spending (to name one) was much higher.
### RE: A coming engineering shortage ? ---- Who agrees ?
"And maybe the need for everyone to get a degree is because of the decline in public school education. The universities are taking over the job of the public schools."
I don't think there's been any evidence given for that claim. Certainly, for most serious, college-bound students, that's definitely NOT the case. When I went to college, back in the dim past, 3 AP classes was above the norm. My high school senior is currently gearing up for his 10th through 14th AP exams. If his competitors were really that poor, there would be no need to stack that many AP classes and exams to be competitive. And even with 9 AP exams with 4s and 5s under his belt, he's barely competitive with his peers.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
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### RE: A coming engineering shortage ? ---- Who agrees ?
@JNieman: here are two figures:
1) Intentions of 4th year engineering students in Ontario, surveyed by Ipsos-Reid on behalf of Professional Engineers Ontario. These surveys have shown results which are consistent through numerous years in which this survey has been completed.
2) Table 1: Match rates between education and employment in all the regulated professions in Ontario, from the 2006 Survey of Households. The 2011 Survey of Households, derived from the long-form census, was destroyed by our former Tory government, deliberately- they found it easier to hold ideologically-based positions when there was no pesky data to contradict them. The current government has fixed that for subsequent years, but the destroyed 2011 census will haunt us for years to come.
A few points:
1) Engineering students in 4th year overwhelmingly want to work as engineers.
2) Over twice as many engineering graduates work outside the engineering profession as work within it. In fact, about 33% of engineering graduates in Canada work in areas of employment for which a university degree of any kind, much less an engineering degree, is not required. That's a larger proportion than the ~ 30% of eng grads who work as enginers
3) The ~70% of engineering grads who work outside the profession, earn on average about 20% less than the ~ 30% who work as engineers or engineering managers
4) The match rate between education and employment for engineering is the lowest of all the regulated professions in the country, and not by a small margin.
The match rate decreases with years of experience, as we all know some people previously employed as engineers who leave the profession either by default or by choice. That fraction is also affected by the influence of immigration: while the situation for engineering grads in Canada in composite is bad, the situation for those Canadian engineers who were educated outside Canada is even worse- of that group, only ~19% work within the profession.
All this adds up to only one conclusion: the engineering labour market for engineering here in Ontario and in Canada in general is saturated, has been saturated for some time, and the saturation has been growing steadily for twenty years. It shows no signs of getting substantially better in the next decade, either.
All this information (the graph previously posted, plus the chart and table posted here) may be found in this report, which I've already linked to- by posting the graphs and charts here, I'm trying to reach the people who haven't bothered to read the report yet:
The report lists all its references and data sources.
### RE: A coming engineering shortage ? ---- Who agrees ?
IR, are you saying that every high school is as good as your local high school?
Strange how some high schools have higher levels of teen suicides than others, and there are few reported school problems.
### RE: A coming engineering shortage ? ---- Who agrees ?
Mine isn't local, we transferred to a different school district. Nevertheless, every high school in our area offers a substantially larger complement of AP classes than ever before, and even the city high school in our old neighborhood offers a large number of AP classes. And this is on top of the IB classes and tests offered. Now, it could possibly be argued that we're in the "one percent" of high schools, being in a relatively rich county, but there are many such high schools across California.
The US News high school report, which we started following in about 2005 timeframe continues listing a huge number of high schools across the US that produce graduating classes with an AVERAGE of 9 AP tests taken. My old high school was among them, so they amped up their game as well. The bottom line is that the good high schools have gotten better, with better college prep than ever before. Rising tide arguments aside, it's possible that the worst high schools have gotten worse, but I have no information about that.
I can say that EVERY UC and Cal State campus is inundated with applicants, and even UC Merced has no problem finding qualified applicants. Note that UC campuses require the infamous a-g high school curriculum, in addition to high GPAs and SAT test scores. UC San Diego, which is nationally ranked, reportedly had over 90,000 applicants for fall of 2017 and had no issue waitlisting people with 3.6 GPA and 34 on the ACT. What used to be "safety" schools are rejecting qualified applicants.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
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### RE: A coming engineering shortage ? ---- Who agrees ?
Something my wife noted while looking for houses a few years ago. The local crime rates are higher around middle and high schools. So maybe those free periods are useful for some of the kids.
Ever since my daughter took the PSAT test last year, she has had hundreds of pieces of mail from differing universities around the country. And several of which I have never heard of.
More recently my daughter had commented that she did not see any calculus on the SAT test she took.
But when you understand that being a social worker also requires a degree, and it does not pay much, one needs to wonder if some university degrees are worth it.
Economics for sure is not on the high school requirement list. So maybe people realize they can make more money with an engineering degree by doing something else.
I hear truck driving pays well, and without the boss always there.
### RE: A coming engineering shortage ? ---- Who agrees ?
"Economics for sure is not on the high school requirement list. "
True, but you can take AP Econ, where offered, which didn't even exist when I went to high school.
But the economics is actually a multiple whammy, given that while there is the requirement for a degree, there's nothing that say that degree has to come from USC or somesuch, but the main issue is that there is such a glut of Psych majors that there's no need to pay them larger salaries.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
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### RE: A coming engineering shortage ? ---- Who agrees ?
A friend of mine is a social worker and makes almost as much me. This is in Canada though so YMMV. Looking at that table I wonder I didn't do PT or something instead...
### RE: A coming engineering shortage ? ---- Who agrees ?
Growing up in NY then living/working elsewhere I have seen firsthand the effects of supply and demand. NY has the proverbial "perfect storm" IMHO, with few exceptions most anywhere you go within the state is <1 hour's drive to a college that offers engineering. The vast majority of them being through the state SUNY system are a great deal for students, live at home or with family cheap and to this day its pretty common for a bachelor's to cost <$30k after all expenses are considered. OTOH, bc of the glut of engineers graduating and industry being taxed out of the state salaries are laughably low. One recent grad I know couldn't "leave home," a BSME only earned him$50k/year, I started $25k higher a decade ago in a dirt cheap section of the Midwest. One point I feel is rarely mentioned/discussed regarding college degrees and licensure is the difficulty level, or IMHO the lack thereof as compared to the reality of design and development. I have mentored quite a few junior engineers and interns who gave up engineering rather quickly bc they did not enjoy the constant challenges, constant learning, or creativity necessary. Like many colleagues who stuck with the profession only to become lousy engineers, they didn't recognize the difference between being a good student and being a good engineer and weren't willing to put in the time and effort to become the later. To a large extent I believe even folks in engineering tend to overplay the accomplishment of earning a degree or license, nevermind the parents, educators, and other non-engineers. Kids tend to be very trusting so its natural that a certain number go into other professions after graduation. ### RE: A coming engineering shortage ? ---- Who agrees ? The difficulty level is interesting. Although I did harder maths at university, by hand, than I ever have since, in practice, say in DSP, I have to know a lot more than just the equations. Same with, say, statics. At uni the problems are known to be solvable, whereas in the real world the list of unknowns often exceeds the knowns. Not that I do much statics as an end result, but it is the starting point for dynamics. For instance suppose we want to design a light subframe that will survive driving through a square edged pothole, yet will fail neatly in a front end crash. The crash guys have a couple of dozen supercomputers and years of experience, they don't need to make reasonable estimates, they can calculate what is going on. The pothole people have a couple of strain gauges on the suspension arms and a force measured somewhere, probably not where it is needed, from one test. Cheers Greg Locock New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm? ### RE: A coming engineering shortage ? ---- Who agrees ? And maybe that's the issue, that so many really don't like the work. ### RE: A coming engineering shortage ? ---- Who agrees ? Lets be realistic, we are consumer and service society, we hardly make things, most engineering solutions are off the shelf, so why people study engineering now a days is beyond me, is hard and the picture at the end, ain't to pretty. ### RE: A coming engineering shortage ? ---- Who agrees ? Less engineering required, and vastly more engineering grads being cranked out. Do the math! ### RE: A coming engineering shortage ? ---- Who agrees ? "Lets be realistic, we are consumer and service society, we hardly make things, most engineering solutions are off the shelf, so why people study engineering now a days is beyond me, is hard and the picture at the end, ain't to pretty." The substation across the street does not look like it was off the shelf. And in fact none of our substations look like they were off the shelf. Maybe parts of it were off the shelf, but it was built by in house crews. ### RE: A coming engineering shortage ? ---- Who agrees ? So how much was engineering and how much trade work? the later is always a local component. ### RE: A coming engineering shortage ? ---- Who agrees ? #### Quote (spraytechnology) Lets be realistic, we are consumer and service society, we hardly make things, most engineering solutions are off the shelf, so why people study engineering now a days is beyond me, is hard and the picture at the end, ain't to pretty. Depends on the definition of "hard" and "pretty." One reason that I enjoy this profession is the variety of both work and people. I've known "engineers" whose day jobs make their undergrad degree seem extremely difficult and others who continually fight a steep learning curve with new technology. Along a similar vein, I know junior engineers earning$50k and several engineers-turned-execs that earn $1M+ annually. ### RE: A coming engineering shortage ? ---- Who agrees ? What about siting of the substation? You can't just plop those things anywhere unless you don't care if they get covered by several feet of water during heavy storms. Just this takes quite a lot of engineering. Sometimes new trenching and building penetrations are needed when changing out equipment, and can the existing bus take the new configuration? This all takes engineering too. Lots of fun! ### RE: A coming engineering shortage ? ---- Who agrees ? For sure there will be some engineering local components that cannot be outsource especially in structural/civil domain but the discussion drifted to engineering in general. Regards. ### RE: A coming engineering shortage ? ---- Who agrees ? #### Quote (moltenmetal) Less engineering required, and vastly more engineering grads being cranked out. Do the math! That smells like lower wages or emigration. ### RE: A coming engineering shortage ? ---- Who agrees ? DISAGREE. As a result of the "Obama economy" - now documented to be the worst in history - I have been out of work as an engineer now for a year and a half. No job in sight. And I know a lot of other engineers in my same predicament. One of my problems: I'm "too old." "No one is completely useless. He can always serve as a bad example." --My Dad ca. 1975 ### RE: A coming engineering shortage ? ---- Who agrees ? IILBAY (((("No one is completely useless. He can always serve as a bad example." --My Dad ca. 1975 )))) I like it, will probably remember it. Thanks. In my case the few opportunities that come across my desk require relocation or being away from home for periods of time. Definitely, good opportunities are far from abound. ### RE: A coming engineering shortage ? ---- Who agrees ? #### Quote (Illbay) As a result of the "Obama economy" - now documented to be the worst in history At the risk of taking this thread off topic, I have to say LOL WHAT? I am no fan of the previous administration policies, OVER ALL, but I can certainly read. Worst economy in history? For WHOM? Rate of growth of USA GDP: http://data.worldbank.org/indicator/NY.GDP.MKTP.CD... https://www.bea.gov/newsreleases/glance.htm https://data.oecd.org/gdp/gross-domestic-product-g... and a more boiled-down explanatory approach here: https://www.bloomberg.com/view/articles/2017-01-19... who places Obama second to Clinton in "best to worst economic performance/strength" during presidential administrations since 1977. For all the fault you can throw out a sarcastic "THANKS, OBAMA!" the economy is one that shouldn't be sarcastic. If you're to lay economic performance on the President, that is. ### RE: A coming engineering shortage ? ---- Who agrees ? When did the dow jones or other indices breaking records indicated the economy is or was terrible? ### RE: A coming engineering shortage ? ---- Who agrees ? A recession is when a lot of other people are out of work. A depression is when I am out of work. Let's show some sensitivity. ### RE: A coming engineering shortage ? ---- Who agrees ? there is little correlation between employment levels and stock market performances. often the working class has little to do or little ability to influence the markets but remember what Stalin said: " death of one person is a tragedy, if many is only statistics " ### RE: A coming engineering shortage ? ---- Who agrees ? I wonder at times what does a young graduate that invested few good years in STEM education, has a nice loan to pay back and suddenly cannot get a job or a start in his/her chosen profession? How frustrating and demoralizing it must be. Any comments? advice,or real life stories ? ### RE: A coming engineering shortage ? ---- Who agrees ? Can't be any worse than a psych major in the same boat, particularly given that the median salary for psych majors is probably about half that of STEM majors, while the loans are probably about the same. There are at least a couple of threads floating around ET from people precisely in the situation. However, there are so many factors both personal and corporate that ultimately determine whether interviews and/or offers come. "I went to a middling university and got middling grades, and now I can't get any responses to my resume," is not an unfamiliar refrain. Supply and demand theory says that only when there's a surfeit of demand will it be likely that all graduates will get hired for jobs they want. The majority of the time, employers are able to pick and choose, and they will often not choose anyone but the very best they can afford. This is not that different that at the start of the college journey, when you get rejected by even your safety schools, and you start looking at whether CC is really where you'll end up for a couple of years and then hope to transfer to a 4-yr college. Or, do you start looking at the colleges that are still taking applicants, even after March 31. I recall a case where a girl failed to get into Stanford, and decided to go there anyway, attend classes, and con people into letting her sleep on their couches because of "housing glitches." She was eventually found out, but I never found out whether Stanford was her reach school or not. TTFN (ta ta for now) I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm ### RE: A coming engineering shortage ? ---- Who agrees ? I know many recent grads and cant say I know any with STEM degrees who were unable to find a job within several months, even in flooded small-town markets during the recession. I also cant say Ive noticed any short term morale or attitude problems amongst them, IME those only develop after years in industry. OTOH, I do know quite a few non-STEM grads who gave up on finding jobs within their field and moved on to others but that is nothing new nor I believe an increasingly common problem. Past generations have struggled with this as well but I believe had a significantly easier time transitioning to other well-paying careers for various reasons, less regulation, less technology, and a significantly better economy being key among many. ### RE: A coming engineering shortage ? ---- Who agrees ? "Any comments? advice,or real life stories ?" I graduated into an awful job market, coming at the end of a recession and following the break-up of Britain's nationalised utilities. The market had a lot of experienced labour looking for work, and the area of the country where I lived was hit hard by major employers closing in mining, ship-building and hevay manufacturing. I took a job with a start-up company making about the same per hour as I had in the bar job I had through university. That job was a great place to learn how a company works and be involved in pretty much all parts of the business except the accounts, but the wages were dire. Took three job moves, a couple of relocations, three good relationships wrecked and two years living out of a suitcase to break into the industry I wanted to be in. I guess the message is that if you want to succeed then you can, but you'll pick up a few knocks along the way. In hindsight was it worth it? Most days, I think I'd say yes. ### RE: A coming engineering shortage ? ---- Who agrees ? The message should be that perseverance and stubbornness can make up for a lot. The people who succeed in the face of huge odds are those that refuse to give up. Naturally, some actual talent would be useful TTFN (ta ta for now) I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm ### RE: A coming engineering shortage ? ---- Who agrees ? Being able to persevere and be stubborn is a blessing and curse. For every guy who has overcome great odds, there are 10 other guys who should have rethought their plan before grinding it to an obvious conclusion. Something has to be said though about lazy people who are smart enough to avoid anything that is too much work. If you are starting a business, your goal should be to pick a specialty that allows you to be as lazy as possible. ### RE: A coming engineering shortage ? ---- Who agrees ? "your goal should be to pick a specialty that allows you to be as lazy as possible." Supply and demand, again. I doubt there are that many specialties that allow you to be that lazy, as it's unlikely that you're the only person in the entire world that has stumbled upon such a gold mine. Some people are simply not able to deal with failures; they wind up in the herd. Others might be too lazy to look for those mythical lazy opportunities. In between are the those that generate the 90% failures in the 1st two years and the 10% that get to fight on, and fraction thereof that succeed for any length of time. Longevity is not necessarily a bulwark against eventual failure, Montgomery Ward was in business over 100 years and even though they attempted to survive as a purely on-line merchant, they still could not overcome their issues. Sears, which is likewise 100+ years in operation is teetering on the brink, although it's managed to last slightly longer than Montgomery Ward. Even Macy's is struggling. TTFN (ta ta for now) I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm ### RE: A coming engineering shortage ? ---- Who agrees ? I graduated within the top 5% of my class, from a top tier university in Canada. I had two years of co-op work experience, and a Master's degree. And it was no picnic for me to find my first job. That was back in 1991, when about 70% of engineering grads in Canada worked as engineers. As of 2011, only about 30% of engineering grads work as engineers. I'd estimate that in Canada, roughly 1/2 the overall graduating class is falling into that disappointment category. They just had to find a job, so they did and moved on. Regrettably though, after two or more years out of the profession, your chances of getting back into it are near zero. Engineering education has a short shelf life. The universities don't even bother to collect the stats on how many of their grads are appropriately employed- they don't care. The ask grads if they're employed, 6 months and 2 yrs after graduation, but don't ask if they're working in the field they were trained for. Instead they ask them a much vaguer question: whether or not their education was "relevant" to their job. Engineering grads are about as likely as the average of all university grads to be employed 6 months or 2 yrs after graduation. Of course that average includes such job magnet programs as fine arts, journalism etc. ### RE: A coming engineering shortage ? ---- Who agrees ? #### Quote: The universities don't even bother to collect the stats on how many of their grads are appropriately employed- they don't care. The ask grads if they're employed, 6 months and 2 yrs after graduation, but don't ask if they're working in the field they were trained for. Sadly we live in a society driven by statistics of low value, so long as the headline looks good the general public is pleased. If you want a real chuckle investigate how universities are "ranked" by the media, things like the pass rate and reputation among college professors all seem like grand ideas but IMHO are rather irrelevant vs bottom line returns like percentage of grads employed in their field within X months of graduation and starting salaries. Having attended the tiny inexpensive local campus of a large state chain system for my undergrad I am rather amazed by the number of folks anymore who correlate attendance cost and university prestige amongst the media to education quality. Sadly I've known quite a few with a MS from a major university who wouldn't have lasted freshman year at "lesser" schools, some schools pass the chaff along with the wheat, others cull it. ### RE: A coming engineering shortage ? ---- Who agrees ? It's not even clear that any of us could get into the schools we originally matriculated. UC Berkeley's statistics show that accepted students' GPAs has steadily increased over the past 2 decades. TTFN (ta ta for now) I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm ### RE: A coming engineering shortage ? ---- Who agrees ? Rabble rabble, back in my day we didn't even have GPAs above 4.0... Rabble rabble... ---- The name is a long story -- just call me Lo. ### RE: A coming engineering shortage ? ---- Who agrees ? It's called grade inflation. Sort of like getting a trophy for showing up, you pass if you show up. After all the students expect something for the money someone pays. Make what you want of that comment. ### RE: A coming engineering shortage ? ---- Who agrees ? My kids took 4 times as many AP exams as I did, so slightly more than grade inflation. We were toying with BASIC; they had AP exams for Java, classes on Python and C#. TTFN (ta ta for now) I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm ### RE: A coming engineering shortage ? ---- Who agrees ? CWB1, I don't know if you end up even with a better engineering workforce if all universities culled a good chunk of their class. There is a huge disconnect between academia and industry. I don't know if a prof. is the best person to weed out all the people who would be better off in something else. I probably would have been culled in my undergrad if the classes in my undergrad that I didn't have any interest in were used to weed out bad engineers Would I have been better for it? I don't know but I doubt it. I do think older engineers have better horse sense. Computers have made people stupid to the point that a lot couldn't tell you what will sort of happen without running a simulation. Be able to run a software package has some how been given the same importance or value as general understanding. I don't know why this is. Maybe, universities should be hammering the basic concepts harder and not go into as much depth. All the deep stuff is forgotten quickly if the foundations aren't understood completely. ### RE: A coming engineering shortage ? ---- Who agrees ? "if all universities culled a good chunk of their class." I don't think that's a good answer. Some of the best students suck at doing actual, real-world, problems. Other of the best students are simply driven by tiger-moms and will suck at engineering, because they have zero passion for it. Early in college is possibly a very poor point in time to determine someone's lifelong fate. My best friend in college didn't decide on his final major until he became a super-senior. Even given all of that, people change and adapt. I don't do anything related to what I majored in, but I'm still happy and I'm very good at what I do now. And, I might actually be sucky at what I majored in. And, I don't see that having more people trained in STEM is necessarily a bad thing. Ignorance of science and engineering can lead to bad or ignorant decisions and decision-making. TTFN (ta ta for now) I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm ### RE: A coming engineering shortage ? ---- Who agrees ? When I did my engineering studies, the university did cull intake and entrance was competitive. What I think happens for some after years of hard work, and not being able to enter the desired field us that it builds frustrations. For sure success is determined by many other factors beyond the degree, like location, field of study, demand, contacts, opportunities and luck. For many, even if they start as engineers, they realize that many and better opportunities are somewhere else and adapt. Maybe that is why I never completed my MS although I did my coursework and have no regrets except for time spent. I was considering a PhD at the time though.Years later I did an MBA and felt I learned something new going beyond engineering. ### RE: A coming engineering shortage ? ---- Who agrees ? HH, JME but schools that cull more students typically graduate better engineers and personally I would sacrifice quantity long before quality. I agree that there is a serious disconnect between academia and engineering but I believe the main reason for this disconnect is the seemingly common notion today that every student who attends deserves a degree. The "great" engineering school my wife attended is an example of this, their relatively high graduation rate and low hiring rates are a function of students having relatively little personal responsibility and being held to relatively low standards. They show up for class, are spoon-fed every detail of testable material, and heaven help the professor whose test questions are more than a renumeration of the few basic textbook assignments theyve had for homework. Forcing the students to think and grow by giving trick or challenging questions is frowned upon and there is little time for discussing the realities of engineering or expounding upon the basic material bc students arent forced to read and learn it outside class as they are elsewhere by the threat of failing. Projects are almost always completed in large groups, common engineering classes often sacrificed for easy "fluff" like six-sigma or OSHA certs, and should the student be dissatisfied with their grade then extra credit and curves are readily available. The university brags about higher GPAs and graduation rates but the reality is their grads trade off education and ability. I have sat through many interviews where students couldnt begin to apply basic principles or couldnt recite them, had only rudimentary knowledge of one solid modeler and common software tools, and little ability otherwise but their resume showed 3.5+ GPAs. Scarily enough, many expect roles in project management or other non-engineering departments but at engineering rates. Its reminiscent of the old joke, "Yesterday I couldnt spell engineer, today I is one." ### RE: A coming engineering shortage ? ---- Who agrees ? "Culling" is not an end-all and be-all. Some of the best engineers I've worked with were rather unimpressive as students, specifically because schoolwork wasn't real-world problems, and they found them boring compared to real-world problems. TTFN (ta ta for now) I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm ### RE: A coming engineering shortage ? ---- Who agrees ? I agree with ScottyUK. There does seem to be a shortage of engineers in the power industry, but only for certain cohorts. This is from the 2015 Center for Energy Workforce Development report on gaps in the energy workforce pipeline: While it is not just for engineers, I'd assume the age distribution wouldn't be too far off. There is a trough in the 37-47 age bracket where the supply of engineers is just low. My anecdotal experience reflects this - like Scotty, I am part of the 37-47 age bracket and had a hard time finding work when I graduated. Luckily, I got a job in the power industry and after gaining some experience, have found no trouble finding work. And it's not because I'm any good either, it just turns out that there isn't that much competition in this age / experience group. For example, at the previous utility I worked at, I was one of only two people in the whole network planning team (of 30+ staff) that was around the same age. Everyone else was either a decade older or younger than us. ### RE: A coming engineering shortage ? ---- Who agrees ? Causes of the trough. 10 years younger = cheaper hires 10 years older = managing dept, living with budget constraints, not hiring enough expensive middle managers. Technology is stealing American jobs. Stop H1-Bs for robots. ### RE: A coming engineering shortage ? ---- Who agrees ? There is definitely a "lost generation" in there- people who weren't hired as fresh grads during poor economic times. Those people moved on to other professions or lines of work. They're gone, and not coming back. Hopefully the firms that became addicted to out-sourcing their entire training cost on others will be wiped out by the coming demographic shift. Perhaps that will finally generate some opportunities for engineers to see rising wages and enhanced working conditions. ### RE: A coming engineering shortage ? ---- Who agrees ? By wiped out by a demographic shift, are you expecting these companies to go out of business? Sorry to say, but rarely do utilities go out of business, and if they do they are taken over by another. Sad to say I have had the same job and pay, but one week the paycheck had one company name, and two weeks later my paycheck had a different company name. Sad to say some of the new people in the industry work for the new energy sources, but don't have many skills that translate to the utility world. Outsourcing would be nice if the outsourcing only included the new documentation requirements of the federal regulations. But sadly, the only ones who understand them are in-house, and already have full jobs. ### RE: A coming engineering shortage ? ---- Who agrees ? Well cranky, it sounds like some people who were lucky enough to get in during those very slow times are going to have the opportunity to be treated like royalty. And they'd better get serious about mentoring and training the next generation on an accelerated schedule! Sounds like a wonderful situation actually- for everybody except the majority of that lost generation. ### RE: A coming engineering shortage ? ---- Who agrees ? The problem is that Power engineering is not available in very many schools. That we are hiring Electricals and teaching them power. ### RE: A coming engineering shortage ? ---- Who agrees ? #### Quote (cranky108) The problem is that Power engineering is not available in very many schools. That we are hiring Electricals and teaching them power. Don't forget, there are a lot of us mechanicals working at utilities too. I have worked for two of the largest power generation utilities in the US (currently at a non-profit co-op district energy plant). I am just on the downward part of the first hump on that chart. It has been quite lucrative for me. ### RE: A coming engineering shortage ? ---- Who agrees ? Hi cranky, That was certainly the case in the UK a few years ago when many polytechnics and universities got rid of their space-hungry, lightly-used power laboratories full of equipment from the 1950's and 1960's and replaced them with other things which squeezed more people into the available space. More bodies meant more money, and it didn't matter because only a half-dozen kids wanted to study an old-fashioned, maths-heavy subject with zero employment prospects. Awkward bastards like me for example - always the black sheep of any group I'm a member of. Today the handful of places here that still have a power engineering program - Bath, Newcastle, Southampton to name a few - are very popular, with graduates being sought-after by the generating and T&D companies and earning good money from the outset. It is a far cry from this industry's darkest days in the late 1980's and early 1990's. Good luck to today's students - power is still (almost) as a tough an option to study as it was back then, and the ones who choose to do so will have to work hard to graduate. ### RE: A coming engineering shortage ? ---- Who agrees ? Hang on, uni isn't a vocational training scheme. Up until recently you couldn't get a degree in Automotive Engineering (and frankly from what I've seen there were good reasons for that), so the first couple of years as a graduate were spent learning on the job, either formally or informally (aka being dropped in the deep end). Cheers Greg Locock New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm? ### RE: A coming engineering shortage ? ---- Who agrees ? That's true Greg, but many universities have shifted their focus toward the microprocessor / telecoms / electronic side of the spectrum - all of which are perfectly valid in their own right - and barely touch the 'old' subjects like electrical machines. Working in generation or T&D is a massive jump for the grads from one of these electronics-biased courses to make, and it's a large training gap for the employer to fill, especially in what has become a very fragmented industry without the large centralised resources of a national or regional utility to provide quality in-house training. Given the choice of paying a relatively small salary premium to grab one of the grads with a power degree or trying to train an electronics grad who never had the chance to study anything in our field, most employers would pay the premium for the power grad because, with all other things equal, the new employee becomes a net contributor more quickly. ### RE: A coming engineering shortage ? ---- Who agrees ? All in all it boils down to a huge disconnect between academia and industry. After all universities will teach whatever is sexy, appealing gets published and brings money in. I remember years ago when there was a push from a university I know to study nuclear engineering, the hype was that going nuclear will be the future of energy. They successfully increase intakes etc....etc. but few years later they had to shutdown the eng dept being left with a narrow PhD program. ### RE: A coming engineering shortage ? ---- Who agrees ? Universities here are going off the deep end with bizarre "specialist" undergrad degrees in order to re-package engineering for an even broader audience (30% of engineering grads working as engineers is clearly too high for them- they're no doubt targeting 15%!) My alma mater now offers environmental (civil stream- they fortunately canned the chemical stream), mechatronics, nanotechnology engineering, management engineering (barf!) and biomedical engineering in addition to the usual civil, chemical, mechanical, electrical, computer, systems design (i.e. industrial) and geological. The previous nuclear specialization died in the '80s. Industry by and large doesn't know what the hell to do with these people. What the unis are doing is hiving off core courses from the underlying discipline and replacing them with courses related to the specialist subject matter. It's not just a matter of taking credit for a few technical electives in 4th year- a chemical stream environmental sacrificed heat transfer as one example. That's a core chem eng course. If they hacked away a couple of the useless higher math courses, pointlessly teaching analytical integration, that would be a different matter! Nobody is getting a nanotechnology specialist job with a B.A.Sc. in nanotechnology. No, you're going to need post-grad to do that- so why RUIN the undergrad degree by chopping core courses? I suppose management engineering (barfs again) seals the transition of engineering from basic training for a profession to "the new liberal arts education", or a sexier business degree. I agree that engineering employers have to produce their own professionals from good raw materials. The university's job is education, not job training per se. And when they try too hard at the job training bit, they fail, badly. What works better? CO-OP work as a mandatory part of the educational process. That actually generates engineering grads who really are able to hit the ground running. ### RE: A coming engineering shortage ? ---- Who agrees ? "Nobody is getting a nanotechnology specialist job with a B.A.Sc. in nanotechnology. No, you're going to need post-grad to do that- so why RUIN the undergrad degree by chopping core courses?" Unclear that this is true, given: http://www.nnin.org/news-events/spotlights/nanotec... TTFN (ta ta for now) I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm ### RE: A coming engineering shortage ? ---- Who agrees ? #### Quote: Nobody is getting a nanotechnology specialist job with a B.A.Sc. in nanotechnology. No, you're going to need post-grad to do that- so why RUIN the undergrad degree by chopping core courses? Why chop core engineering classes? To make the overall program easier thereby improving GPAs and graduation rate, thereby improving the school's ranking in irrelevant media reports. "Nanotechnology" also makes for better advertising than "mechanical engineering" to the ignorant. ### RE: A coming engineering shortage ? ---- Who agrees ? I am amazed when I see from time to time new names for new engineering disciplines, nanotechnology, mechatronics, materials, bio, etc that are nothing but a surrogate of core competencies in basic engineering. As a matter of fact I recall graduates years ago coming out into the market place with new engineering titles and potential employers asking "what is that ?" Some of the degree may fit into an academic setting ; not always an industrial one. ### RE: A coming engineering shortage ? ---- Who agrees ? Nanotechnology is quite different that traditional mechanical engineering, so I'm not sure why one would think it's simply an advertising gimmick; it's a multidisciplinary function that involves electricity, chemistry, quantum mechanics, and physics at the molecular level. A quantum dot has no corollary in large scale engineering. Quantum dots are being applied to industrial applications at this instant, so it's not an academic subject. We were looking at sprinkling quantum dots on persons of interest to track their movements nearly 10 years ago. The discussion above about power engineering is an example of the specialization that has already occurred in the electrical engineering arena. 70 years ago, there wasn't much to distinguish power EEs for other EEs since they all wound up taking the same basic courses. Today, an integrated circuit design EE would probably have very little overlap with a power EE. I had many courses on transistor (bipolar and MOS) circuit design and modeling, while 70 years ago, the bipolar junction transistor had barely been invented and the MOS transistor wasn't to make its debut until about 55 years ago, and a whole new field of physics and engineering had to developed to support the industrial needs of those devices. TTFN (ta ta for now) I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm ### RE: A coming engineering shortage ? ---- Who agrees ? ok, so how many jobs you see advertised in nanotechnology for a graduate engineer? zero, maybe if lucky he/she can get a job as a research assistant or as a grad student. Lets be realistic, better to have a degree in core engineering discipline and let life take you where it takes you. ### RE: A coming engineering shortage ? ---- Who agrees ? MFJ, I agree there are many mechanical engineers, and civil engineers in the power area, and as many of us are on the top of the red curve, there will be a shortage. Also as government requirements are ramped up, the shortage is starting now. But just a question about why we are not hearing about robotics engineers, or shortages in that field? And maybe because robotics is covered by another type of engineering. ### RE: A coming engineering shortage ? ---- Who agrees ? IRStuff, you've just proven my point. Nanotechnology is a good specialization for a masters or PhD level student, after a degree in chemical, mechanical or perhaps electrical engineering. I can tell you that my alma mater struggles to find co-op jobs for their nanite undergrads, and we see many former nanites transferring back into chemical after a few terms after waking up and smelling the cat food. ### RE: A coming engineering shortage ? ---- Who agrees ? Aren't going to see too many PhD's being CAD jockeys. Our efforts in quantum dots were all purely engineering aspects of how to disperse them covertly and track them, well within our lowly Bachelor's degree purview. TTFN (ta ta for now) I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm ### RE: A coming engineering shortage ? ---- Who agrees ? Another spin here is immigration. If we look at Canada, Australia New Zealand and US, the first 3 have a rather liberal policy that brings in an oversupply of engineers and other professionals well and above the local needs. In US where the policy is restricted it does not really have an impact on supply. ### RE: A coming engineering shortage ? ---- Who agrees ? From time to time I get emails from recruiters I do not know or do not remember ever contacting. Nevertheless the note had a positive spin: "It’s pretty obvious, your time is now! Positions are hard to fill, salaries are on the increase and you want to make sure that you do not miss the opportunity to position yourself in the right role, with the right salary and the right future career prospects so you can also benefit and prosper over this next boom period. How you do this, is where it gets a little complex - if you are in a role now where you really feel that the role equals the rewards, good for you, however if you have been in a role for a while with no salary or career review, you should be questioning your employers commitment to you. " We are all very well aware that the Australian Construction Industry is on the precipice of an unprecedented period of significant growth in NSW/Victoria and SA in delivering Road/Tunnel/Rail Transport infrastructure Projects over the next decade. It is exciting that we are in one of the key industry sectors along with the Health (health and aging population), Wealth (Management), Logistics, Tourism and Education that is going to drive the economy for the next 10 years or so. When it comes to staff recruitment and retention, this Transport Infrastructure boom is going to bring some significant challenges to Engineering and Construction Groups of all sizes, as experienced previously in the mining and oil and gas boom. .....already seeing talent shortages growing already in many areas such as PM (especially RMS experienced), SPE-PE and Supervisors (where have they all gone?). I have recruited specifically in this sector for 30 years and I predict that the next 1-3 years will be the most challenging period ever when it comes to Civil Construction recruitment as there seems to be too much work to do with too few resources to deliver. It is also important to remember that Australia is not the only Country with this issue, as Globally the Construction sector is predicted to grow by 85% to$15.5 trillion by 2030 so the usual recruitment drives to the UK, RSA and UAE will not deliver the same successful outcomes as was achieved previously.
So what does this mean for you as an extremely valuable, scarce and local individual with a strong career to date and demonstrated experience delivering Transport Infrastructure Projects?
It’s pretty obvious, your time is now! Positions are hard to fill, salaries are on the increase and you want to make sure that you do not miss the opportunity to position yourself in the right role, with the right salary and the right future career prospects so you can also benefit and prosper over this next boom period. How you do this, is where it gets a little complex - if you are in a role now where you really feel that the role equals the rewards, good for you, however if you have been in a role for a while with no salary or career review, you should be questioning your employers commitment to you.
This is a hard and challenging industry with long hours, high pressures and expectations and all under tough and demanding circumstances so it is important that you feel comfortable that you are being acknowledged and looked after by your employer, and if you aren’t - there are plenty of opportunities out there for you!
### RE: A coming engineering shortage ? ---- Who agrees ?
#### Quote (spraytechnology )
If we look at Canada, Australia New Zealand and US, the first 3 have a rather liberal policy that brings in an oversupply of engineers and other professionals well and above the local needs. In US where the policy is restricted it does not really have an impact on supply.
### RE: A coming engineering shortage ? ---- Who agrees ?
Mine's always been cash in my pocket regardless the name, never had a moving expense otherwise and wasnt sure what other moving benefits the Silicon Valley set get. Granted its not a year's salary but still a nice little bonus. Perks like this often make me wonder why so many younger engineers seem afraid of change. I've volunteered for layoffs twice where I knew I was getting 6+ months salary as severance, "moving" bonus, and leaving on a Friday with a better position waiting Monday.
### RE: A coming engineering shortage ? ---- Who agrees ?
In 2014, I got a 25K signing bonus and just over 45K for moving expenses. In 2016, I got a 5K signing bonus (along with a 15% increase in pay over previous employer) at another local company. I agree with CWB1, not sure why people are afraid of change. I think most people are willing to accept the status quo and/or don't want to put in the effort to make something happen. Doing that will usually limit your growth. An example, I started at an EPC at the same time as another engineer in 2011. Our salaries were within 3K of each other. Now six years later his salary has increased ~ 22%. I am at my third different company since then and my salary has increased by just over 100%. He is one of those people that is content with being a "company guy" and doesn't care to look for anything else. He will probably work at the EPC for as long as they stay in business, for better or for worse. A lot of people under 40 seem to have that same view. They seemed thrilled to just to have a job and act like these companies are doing them a huge favor.
### RE: A coming engineering shortage ? ---- Who agrees ?
Good info folks, obviously I'm in the wrong part of the country/world!
### RE: A coming engineering shortage ? ---- Who agrees ?
"They seemed thrilled to just to have a job and act like these companies are doing them a huge favor."
That's not necessarily the only reason for not changing jobs:
> commute -- yes, I could change jobs if I were willing to put up with a 1hr+ one-way commute, but that's nowhere within my cost/benefit analysis space. I could move, but I like my house more than I like any company that's not within a reasonable commute
> starting over -- a new job entails a significant time to build up one's creds and reputation; often, one enters a new job essentially as a noob in the pecking order. Finding your new spot takes time and energy, neither of which I want to expend at this point in my career
> crappy people, etc. -- when you find a job where the crackheads and difficult people are gone, for whatever reason, that's hard to give up. Going to a new job entails the possibility of running into, and afoul of, self-centered nitwits, idiots, and other forms of lower life. These are chi-vampires; they suck your energy and give you nothing in return. You can't be sure of running across them during a single day interview, so it's a gamble. Often, you don't even find them until re-orgs and whatnot shake them loose from the woodwork, and you find yourself writing Pearl Harbor memos and pondering when to give them the finger and walk out.
I've changed jobs 7 times, more or less, not always voluntarily, and there have been at least few times in previous jobs where the above bullet points were true. There's one guy in the current company that's a bit of a chi-vampire, but only because he whines about having never done something before, which is a real motivation sink during a proposal. But, he's not always on my proposals, so I can live with that.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm
### RE: A coming engineering shortage ? ---- Who agrees ?
I have to agree with some comments above; generous bonuses are common in US, less if any in other parts of the world, meaning there are more lucrative opportunities in US for employees.
IRstuff - I like your comments about " crappy people" oh boy .... when you come across toxic people my best advice is ...run. Life is to short to put up with that.
### RE: A coming engineering shortage ? ---- Who agrees ?
#### Quote (IRstuff)
That's not necessarily the only reason for not changing jobs:
> commute
> starting over
> crappy people, etc
Of course there are other factors to be considered when contemplating a job change and each one should carry some weight. I always factor those in as well. I have excel spreadsheets that I made for economical analysis that include commuting costs, time spent on work related activities (commute + expected hours at work), benefits costs, state and local taxes, etc. Luckily, I don't mind the starting over part since I tend to make an impact and get noticed for my abilities rather quickly. Could that not be the case somewhere, sure, but so far, it has always worked out that way for me. As for people, I just see people as people. I don't expect to go anywhere to make new friends. I just keep it work related and build good working relationships. This has also proved very successful for me.
All that said, I have turned down significantly more jobs than I have accepted due to commute considerations and/or vibe I got during interviews. The current place I work now had some questionable individuals that I met during the interviews and it increased commute from 7 miles to 33. I was on the fence on this one, but I saw the potential and it has been a great job change.
### RE: A coming engineering shortage ? ---- Who agrees ?
I don't think most take issue with older folks settling or even "coasting" to retirement (within reason), but for engineers fresh out of college its pretty detrimental to their career IMHO.
### RE: A coming engineering shortage ? ---- Who agrees ?
Hey!!! you calling me old?
Well...
I resemble that remark.
The bottom line is that some people love change, are adrenaline junkies, or they're ambivalent, or they hate change. It takes all kinds of people to make a good team. Having no tribal knowledge can be a really bad thing. There needs to be some old curmudgeonly geezer that can tell you, "oh yeah, we did that 15 years ago, and here's why that was a disaster." That actually happened, but the old geezer was only IBM Tech Systems Journal that had a paper from 15 years prior explaining why we were \$3M in the hole because some lame maintenance guy decided to monkey with the previously qualified and working process.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm
### RE: A coming engineering shortage ? ---- Who agrees ?
Engineers, as a group, tend to be negative and I've heard that comment from quite a few non-engineers. Life is never so bleak as some think, including me. And life is very hard for me right now so I am no Pollyanna.
Whether there is a shortage or not, nature and nurture will still effect engineering. People usually move towards their desires even when outside motive forces are not acting upon them. In short, I don't know that we have that much control over numbers in the profession. We do not need to sell young people on STEM. We need to educate them about it enabling them to make a good decision for their lives. It's not about us but them and their interests. We've made our decisions.
I've been participating in the Central Chapter of NSPE-CO, since 2014. It's been quite an education. I understand the importance of licensure and membership in NSPE better now and I am still learning. It is interesting to listen to engineers, attorneys, and insurance companies discuss problems that arise and how they are dealt with, in and out of court. One engineer has been in court numerous times on various things and always takes in a wagonload of documentation and ensures he is familiar with his wagonload of documentation. It matters and is not insignificant. There are many such stories engineers tell about this kind of thing. Attorneys and insurance companies have some interesting stories.
With changes coming in technology, I believe licensure will become even more important and widespread. At least one old industrial company has done away with the industrial exemption and spent several hours explaining what that meant to their engineering staff. With autonomous vehicles coming, based upon some of the presentations I've heard on it, the automotive industry will probably change. I don't know how ubiquitous that thinking is as it is just my opinion based upon what I've learned in the last 4 years of membership in NSPE. My former employer didn't want to assume the legal responsibilities for its engineers any longer and I cannot believe others will not follow suit.
Licensure in the USA is rooted in the US Constitution through Amendment 10 as well as Article 4, Section 2. With that in view, I foresee licensure for engineers as transportation technologies advance.
When I researched ABET's and NCEES's websites, I began to realize that licensure is not insignificant because a lot of effort goes into making it possible. It provides a standard to measure competence much like licensure for physicians and attorneys. And for those who don't put much stock in standards, let's go back to no standards on threads, fiber, etc. and see how good everything works. I know there are problems everywhere but it's a place to begin.
Life events are seldom simple and people are seldom simple. The state of industry, engineering, society, etc. are due to a host of factors, to me. In the USA, a general coarsening of our society has occurred over my lifetime, which is disheartening. We don't value human capital. We have isolated ourselves into silos, which is destructive. This statement reflects some of what I see, "I just don’t understand the disrespectful attitude toward working people.” Source: AFL-CIO CEO-Worker Pay Ratio
Pamela K. Quillin, P.E.
Quillin Engineering, LLC
NSPE-CO, Central Chapter
### RE: A coming engineering shortage ? ---- Who agrees ?
I've heard the suggestion that engineers are negative before. I disagree, although I understand where the perception comes from.
We're the ones who see the practicalities and the difficulties in doing something, and we speak up about those things because we understand them. In the eyes of the dreamers we're negative because we shoot holes in their ideas right at the outset. I actually think we're some of the most positive people out there: the optimists who say "Yeah, it hasn't been done before, but we'll find a way to make it work even though we aren't sure quite how." Our underlying optimism is often masked by other traits though, like the cynicism which often develops after a few years in the business, and our seemingly dogmatic application of 'the rules'.
We don't help our cause much do we?
### RE: A coming engineering shortage ? ---- Who agrees ?
I have noticed a trend I call 'magical thinking'. Somebody assumes some outcome they'd like to see, as an enhancement on the present state, and it becomes the foundation of some future state. The ballbusters amongst us then point out that while FS is a nice goal, PS to FS is not just a case of waving a wand and shouting some hokum Latin, but may involve spending money, time, resources, at the very least, might need to break a few physical laws, and will have unintended consequences. This makes said ballbusters unpopular with politicians, Social Justice Warriors, and the Twitterati.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
### RE: A coming engineering shortage ? ---- Who agrees ?
What's worse is if you can think of the objections and reasons for failure faster than the proposer can even complete their presentation. For some peculiar reason, they think that we are not only negative, but we're close minded.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm
### RE: A coming engineering shortage ? ---- Who agrees ?
ScottyUK, no we don't help our cause much.
We do see a lot others don't but, even when they do see things correctly, we often shoot holes in their ideas and them.
Pamela K. Quillin, P.E.
Quillin Engineering, LLC
NSPE-CO, Central Chapter
### RE: A coming engineering shortage ? ---- Who agrees ?
"We do see a lot others don't but, even when they do see things correctly, we often shoot holes in their ideas and them."
Yeah, BTDT; it works great with SWMBO
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm
### RE: A coming engineering shortage ? ---- Who agrees ?
IRstuff, are you still surprised to be alive?
Pamela K. Quillin, P.E.
Quillin Engineering, LLC
NSPE-CO, Central Chapter
### RE: A coming engineering shortage ? ---- Who agrees ?
I came across a 'brain storming' session white board that had not been erased. It was apparently from the new-grad bunch being groomed to meet the needs of the Fearless Leader**. One of the entries was "Gundam Suit." Nothing like introducing Japanese Anime as a possible future product. The old guys might have been negative about that sort of idea.
One thing that I've considered in such things is that the person who is floating an idea has never asked the basis questions.
1) Why has no one else thought of this?
2) What do I know that no one else does?
As long as the answers relate to corporate inertia or being the first to the party then there's a chance to succeed. Apple computer, for example, benefited greatly from IBM's inertia and Google was the first to understand the page-rank concept.
But what kills me is when someone is basically saying they are so smart that they alone, with no research at all, have concluded that some idea is the best idea. And I find the reason they think they are so smart is they have done nothing to build a basis of comparison.
**The management guy who was leading this also led a project that 3 of 3 engineers said was a bad idea and forced me to use a mechanism I was told later had failed in a prototype stage but they didn't pass that information along to me before demanding I design using it. What was interesting is the core component was purchased from a company that had motive to design a system just like the management guy was going for, but he failed to ask either question. As soon as it was all assembled, it immediately failed and they threw 3-4 years worth of my salary in the garbage and pretended it didn't happen.
I could have saved that company a lot of money by just not working on what the dreamers came up with.
### RE: A coming engineering shortage ? ---- Who agrees ?
"are you still surprised to be alive?"
My florist bill is rather high
We used to have a guy who was the gatekeeper for IR&D (independent research and development), always has two showstopper questions. When we first went to him for a new project, he'd ask, "Is anyone else doing this?" We answer "no," and he'd say, "then why do we want to be the first?" Next time around, he'd ask his same question, and we'd answer "sure, A and B are both pursuing it." He'd then say, "so why do we want to be doing the same?"
So, those are always good questions, "are we really the only people the universe to have thought of this?" and, "if this is really a good idea, why aren't there more people doing it?"
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm
### RE: A coming engineering shortage ? ---- Who agrees ?
2
One of my pet peeves is a closely related cousin to Greg's "magical thinking" and seems to be the polar opposite and enemy of objective (some say negative) debate of a project's merits. I call it "powerpoint engineering" whereby someone with an engineering title, CAD suite, and usually some sort of basic analysis program that they do not actually understand makes a lot of pretty presentations that convince management they are going to make the company billions. They then enjoy many months/years being billed as a rising leader within the company and usually do their best to limit invitations to design reviews, other technical, and DFMEA discussions to prevent technical experts from attending. If the chief powerpoint engineer is in-house they often move to a sister company, division, or other distant department shortly before the recalls and warranty claims begin, and often do so with a raise or promotion. If the chief powerpoint engineer is good they also get an important executive to attach their name to the project so its eventual failure is guaranteed to quickly be explained away and forgotten. If the powerpoint engineer is an outside contractor we commonly call them a consultant, pay them 3x as much as necessary, give them 5x as much time to work, and usually have little/no recourse for substandard work and lack of results. Not to suggest all consultants are that bad, but I've come across enough in aerospace and automotive that whenever the word is mentioned I admittedly get a bit cheeky and counter with suggesting more interns or junior engineers be hired instead. I believe this is where the many jokes and stereotypes about PEs stem from, and why I question the long term viability of keeping the current licensing system. In many regards PEs are starting to go the way of the union journeyman's card as a serious sign of incompetence creating distrust despite being intended to do the opposite.
### RE: A coming engineering shortage ? ---- Who agrees ?
#### Quote (CWB1)
One of my pet peeves is a closely related cousin to Greg's "magical thinking" and seems to be the polar opposite and enemy of objective (some say negative) debate of a project's merits. I call it "powerpoint engineering" whereby someone with an engineering title, CAD suite, and usually some sort of basic analysis program that they do not actually understand makes a lot of pretty presentations that convince management they are going to make the company billions. They then enjoy many months/years being billed as a rising leader within the company and usually do their best to limit invitations to design reviews, other technical, and DFMEA discussions to prevent technical experts from attending. If the chief powerpoint engineer is in-house they often move to a sister company, division, or other distant department shortly before the recalls and warranty claims begin, and often do so with a raise or promotion. If the chief powerpoint engineer is good they also get an important executive to attach their name to the project so its eventual failure is guaranteed to quickly be explained away and forgotten. If the powerpoint engineer is an outside contractor we commonly call them a consultant, pay them 3x as much as necessary, give them 5x as much time to work, and usually have little/no recourse for substandard work and lack of results
Tone the sarcasm down a little. Tell us what really happened.
### RE: A coming engineering shortage ? ---- Who agrees ?
Plazma, there was nothing in that post intended to be sarcastic. My response to outside hiring is a bit facetious but also very serious. I am not discussing an isolated incident but quite a few that I have witnessed at several large corporations and after discussing with peers have come to realize is common occurrence. I have no problem with internal subject matter experts with well-proven history and experience taking charge of their area of expertise nor competent outside help, but there are many inexperienced phonies in industry as well that are mistakenly put into positions of significant responsibility.
One good example was my last employer outsourcing the design of a new variety of widget rather than hiring internally. The firm hired had no experience in that area and after a few initial concept reviews it became painfully obvious their analysis was flawed. It became a "us vs them" scenario but because management had pitched their involvement as beneficial and contracts signed, internal experts were excluded and their opinions were dismissed, and the powerpoint engineers continued unabated. More than a year later the predicted project failure occurred and the company had no recourse. The failure was swept under the rug as being due to insurmountable issues when in reality it failed due to incompetent engineering. Others may disagree, but I am very careful to take unsupervised design responsibility only on things which I have experience with as I view it unethical to work outside my area of experience. Garbage in and a pretty picture out does not make a successful test, and many things cannot be learned except by experience testing what works and what does not. If I was risking only my own money and time that would be one thing, however doing so for an employer or client is quite another.
### RE: A coming engineering shortage ? ---- Who agrees ?
It is rather known fact in particular in large organizations, that incompetent people get " promoted up" to get rid of them.
Often the attempt is to promote them in a role they cannot make much damage, not always the case.....
### RE: A coming engineering shortage ? ---- Who agrees ?
Don't you hate the know it all, because you can't teach him anything.
But often real learning happens when he has to fix his own mistakes.
Shortages happen when companies are not willing to create training positions. There may not be a shortage of newbees, but there will be a shortage of knowing olders soon enough.
### RE: A coming engineering shortage ? ---- Who agrees ?
The best engineer I have met was beyond arrogant. I don't think anyone taught him anything. He was too prideful to not just figure out himself or to fail. I don't know how much stuff he screwed up but I don't think it was much. He thought he knew everything and went off with another guy to start a consulting company. It worked out for him so maybe he did.
### RE: A coming engineering shortage ? ---- Who agrees ?
I wonder if this topic can be tied to HR non-sense?
God made the integers, all else is the work of man. - Leopold Kroenecker
### RE: A coming engineering shortage ? ---- Who agrees ?
No, this goes beyond HR, as exemplified by our president's latest immigration proposal; obviously some birdies whispered in his ear that there is a shortage of English-speaking skilled labor in the US.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm
### RE: A coming engineering shortage ? ---- Who agrees ?
amp/spectrum.ieee.org/riskfactor/at-work/tech-careers/exposing-the-roots-of-the-perpetual-stem-crisis-.amp.html
I don't think I'm going to run out and snap up the hard-copy, mostly because I don't have access to the waiting rooms or parlours where it would be best skillfully and artistically placed.
(If this shows up as shouting, forgive my less-than mastery of Chrome in the real world)
.
(Me,,,wrong? ...aw, just fine-tuning my sarcasm!)
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2018-01-19 03:53:39
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https://indico.uu.se/event/317/contributions/297/
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Use Single SignOn (SSO) to login with your home institute's account and login service.
# 20th European Young Statisticians Meeting
14-18 August 2017
Uppsala University
Europe/Stockholm timezone
## Confidence regions in Cox proportional hazards model with measurement errors
17 Aug 2017, 16:00
30m
Ångströmslaboratoriet ()
Speaker
### Speaker
Ms Oksana Chernova (Taras Shevchenko National University of Kyiv)
### Description
Cox proportional hazards model with measurement errors in covariates is considered. It is the ubiquitous technique in biomedical data analysis. In Kukush et al. (2011) [ Journal of Statistical Research **45**, 77-94 ] and Chimisov and Kukush (2014) [ Modern Stochastics: Theory and Applications **1**, 13-32 ] asymptotic properties of a simultaneous estimator $(\lambda_n;\beta_n)$ for the baseline hazard rate $\lambda(\cdot)$ and the regression parameter $\beta$ were studied, at that the parameter set $\Theta=\Theta_{\lambda}\times \Theta_{\beta}$ was assumed bounded. In Kukush and Chernova (2017) [ Theory of Probability and Mathematical Statistics **96**, 100-109 ] we dealt with the simultaneous estimator $(\lambda_n;\beta_n)$ in the case, where the $\Theta_{\lambda}$ was unbounded from above and not separated away from $0$. The estimator was constructed in two steps: first we derived a strongly consistent estimator and then modified it to provide its asymptotic normality. In this talk, we construct the confidence interval for an integral functional of $\lambda(\cdot)$ and the confidence region for $\beta$. We reach our goal in each of the three cases: (a) the measurement error is bounded, (b) it is normally distributed, or (c) it is a shifted Poisson random variable. The censor is assumed to have a continuous pdf. In future research we intend to elaborate a method for heavy tailed error distributions.
### Primary author
Ms Oksana Chernova (Taras Shevchenko National University of Kyiv)
### Presentation Materials
Paper
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2021-01-24 13:18:38
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https://math.stackexchange.com/questions/4027955/the-point-of-intersection-of-tangents-of-a-circle-and-the-circumcircle-formed-by
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# The point of intersection of tangents of a circle and the circumcircle formed by the points of contact and the center of the original circle.
I just wanted to know how this result is derived.
Let there be a circle whose equation is $$x^2+y^2=a^2$$. Let there be a chord PQ. If we draw the tangents from points P and Q they will intersect at a point (say, T). Now if we construct the circumcircle of the triangle OPQ ( O being the center of the initial circle), then Why is it so that T lies on the circumcircle of the triangle OPQ? I have already tested this result several times but can't figure out the derivation...
• $OPTQ$ is cyclic becuase $OP \perp PT$ and $OQ\perp QT$. Feb 16, 2021 at 15:58
The circumference centered at $$T$$ with radius $$TP$$ is orthogonal to the circumference centered at $$O$$ with radius $$OP$$.
Let me first recall this very elemental geometry Theorem: Let $$C$$ be a circumference and let $$P$$, $$Q$$ and $$R$$ be points in $$C$$ with $$P$$ and $$Q$$ diametrically opposite. Then the angle $$\angle{PRQ}=90^º.$$
With this being said, in your problem, the angle $$\angle{OPT}=90^º$$ (by the way you defined $$T$$). By the Theorem, $$O$$, $$T$$ and $$P$$ are in a circumference ($$C_1$$) where $$OT$$ is a diameter. By the same reasoning, the $$\angle{OQT}=90^º$$ and therefore $$O$$, $$T$$ and $$Q$$ are in a circumference ($$C_2$$) where $$OT$$ is a diameter. Finally, since $$C_1$$ and $$C_2$$ contain $$O$$ and $$T$$ and have the same diameter, then $$C_1$$ and $$C_2$$ are the same. Therefore $$O$$, $$P$$, $$T$$, and $$Q$$ lay on the same circumference.
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2022-07-01 23:53:03
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https://math.stackexchange.com/questions/3544734/why-is-the-projection-of-an-area-over-a-plane-the-same-as-the-projection-of-a-ve
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# why is the projection of an area over a plane the same as the projection of a vector normal to the area with length equal to that area.
I'm trying to find some proof or any intuition behind the property explained in the following document.
I find (c) hard to accept, what's the relationship between the amount of surface perceived at a certain angle and the component of the area as a vector in that direction? I understand it "feels" right but I can't quite find an explanation of why this is the case.
Original document here
Edit: I noticed that wikipedia also mentions this, but no explaination or proof is offered
I assume that you are OK with parts a and b. Now let's develop an intuition about part c. In the first instance, let's simplify the problem even more. Assume that the tilt is around the horizontal axis. So the normal to the plane makes an angle $$\theta$$ with the horizontal. The bottom part of the paper (say length $$l$$) will not change its apparent size when the rectangular piece of paper is tilted. The vertical side of the rectangle, $$L$$, when tilted an angle $$\theta$$ will change its apparent size to $$L\cos\theta$$. The apparent area of the rectangle is now $$dS'=lL\cos\theta=dS\cos\theta$$ Now let's get back to the original statement, by rotating the tilted piece of paper around the axis towards the eye. Notice that the normal to the paper is still at angle $$\theta$$ with respect to that axis (it moves over the surface of the cone with half angle $$\theta$$). Also, due to symmetry, the apparent area $$dS'$$ does not change with this additional rotation. Therefore part c is proved.
In the figure above, initially the piece of paper is vertical (as seen from the side). The length $$L$$ is along the $$OA$$ axis, $$l'$$ is perpendicular to the figure (out of the image). The original normal to the paper points along $$B$$ (towards the eye). In the first case I've rotated the paper along the axis through $$O$$, perpendicular to the figure, by an angle $$\theta$$. That moved $$B$$ to $$B'$$ (direction of the normal changed by $$\theta$$) and $$A$$ to $$A'$$ (also by angle $$\theta$$). To prove that both angles $$\angle BOB'$$ and $$\angle AOA'$$ are the same, just use the fact that adding $$\angle B'OA$$ to both of them yields $$90^\circ$$. That means that the apparent size of $$A'O$$ is the vertical projection $$A'O\cos\theta$$.
For the last part, I took the above figure, and rotated around the $$OB$$ axis, in such a way that the $$OB'$$ describes the surface of the cone with vertex at $$O$$. No matter where on this cone you put $$B'$$, the angle between $$OB'$$ and $$OB$$ is unchanged.
• why is $\theta$ on the second term equal to the $\theta$ on the third term? unless im not visualizing correctly the first $\theta$ is between the plane of the projection and the plane observed, while the second $\theta$ is between the axis of rotation and the normal (thats always 90 degrees, right?) imgur.com/VQtKq8E – Joaquin Brandan Feb 13 '20 at 4:33
• If you tilt the plane an angle $\theta$ away from the vertical direction, it's normal is also moving by angle $\theta$ (away from the horizontal). I will attach a figure to my answer in a few minutes – Andrei Feb 13 '20 at 4:48
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2021-01-27 14:37:31
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http://en.wikipedia.org/wiki/Coplanarity
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# Coplanarity
In geometry, some points in space are coplanar if there is a geometric plane that includes them all. For example, three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. However, a set of four or more distinct points will, in general, not lie in a single plane.
Two lines in three-dimensional space are coplanar if there is a plane that includes them both. This occurs if the lines are parallel, or if they intersect each other.
Distance geometry provides a solution technique for the problem of determining if a set of points is coplanar, knowing only the distances between them.
## Properties
In three-dimensional space, two independent vectors with the same initial point determine a plane through that point. Their cross product is a normal vector to that plane and any vector orthogonal to this cross product through the initial point will lie in the plane.[1] This leads to the following coplanarity test. Four distinct points, x1, x2, x3 and x4 are coplanar if and only if,
$(x_3 - x_1) \cdot [(x_2 - x_1) \times (x_4 - x_3)] = 0.$
If three vectors $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are coplanar, then
$(\mathbf{c}\cdot\mathbf{\hat a})\mathbf{\hat a} + (\mathbf{c}\cdot\mathbf{\hat b})\mathbf{\hat b} = \mathbf{c},$
where $\mathbf{\hat a}$ denotes the unit vector in the direction of $\mathbf{a}$. That is, the vector projections of $\mathbf{c}$ on $\mathbf{a}$ and $\mathbf{c}$ on $\mathbf{b}$ add to give the original $\mathbf{c}$.
## Coplanarity of points whose coordinates are given
In coordinate geometry, in n-dimensional space, a set of four or more distinct points are coplanar if and only if the matrix of the coordinates of these points is of rank 2 or less. For example, given four points, W = (w1, w2, ... , wn), X = (x1, x2, ... , xn), Y = (y1, y2, ... , yn), and Z = (z1, z2, ... , zn), if the matrix
$\begin{bmatrix} w_1 & w_2 & \dots & w_n \\ x_1 & x_2 & \dots & x_n \\ y_1 & y_2 & \dots & y_n \\ z_1 & z_2 & \dots & z_n \end{bmatrix}$
is of rank 2 or less, the four points are coplanar.
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2014-10-21 15:44:13
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https://www.allaboutcircuits.com/news/voyager-mission-anniversary-celebration-long-distance-communications/
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The Voyager spacecraft are on a long journey out of our solar system into interstellar space. Despite their great distance from Earth, we are still able to communicate with the spacecraft on a regular basis. This article looks at the basic communication infrastructure that allows us to communicate with the spacecraft.
Welcome to AAC's series of articles celebrating the Voyager missions! Check out the other articles in the series to catch up:
This week, series coordinator Mark Hughes looks at the long-distance communications the Voyager craft are equipped with.
### The Deep Space Network
After the Voyager spacecraft left Earth and completed their grand tour of the solar system, they began their journey into the regions of space that are beyond the influence of our sun—answering questions about what lies in the great cosmic void between stars.
Thirty-eight hours ago, a 20 kW signal was transmitted from Earth towards the Voyager 1 spacecraft. Nineteen hours ago, the signal was received by Voyager 1 and returned by a 20 Watt transponder. And, as I write this article, a station in Madrid, Spain is receiving that return signal at a power level of $$9\times10^{-23} \text{kW}=9\times10^{-8} \text{pW}$$ (-160.48 dBm.) For reference, a very good FM radio receiver can pick up signals at $$9\times10^{-5} \text{pW}$$, the signal received from Voyager is 1000 times weaker.
##### Accelerating Image showing the path of the Voyager spacecraft and the planets during its mission. Credit: Mark Hughes
The Deep Space Network consists of three antenna complexes that are stationed around the globe approximately 120-longitudinal degrees apart. The global separation of stations allows most spacecraft to have an uninterrupted line-of-sight with at least one station regardless of the time of day. A listening station will rise before the last visible one sets. Voyager 1 is still visible from all three stations, but Voyager 2 is only visible from the Canberra, Australia site.
##### This spinning globe has red dots that represent Deep Space Network stations in: Canberra, Australia; Goldstone, California, United States; and Madrid, Spain. Credit: Mark Hughes
Watch which spacecraft the Deep Space Network antennas are communicating with below.
##### Visit the full website: https://eyes.nasa.gov/dsn/dsn.html
As the spacecraft travel further from Earth, the signal strength decreases due to free space path loss. Data rates typically fall as a consequence. Improvements in the Deep Space Network receiver sensitivity over the past 40 years have mitigated reductions in data rate.
##### Deep space network capabilities. Image credit: NASA.gov
Due to the incredible weakness of the spacecraft's downlink by the time it reaches Earth, large parabolic reflectors, and hyperbolic sub-reflectors collect the microwave radiation and focus it on a cryogenically cooled receiver at the base of the antenna.
##### Image of a microwave antenna from NASA.gov. Click here for a larger detailed image of the antenna.
Each Deep Space Network location has multiple 34-meter antennas and a single 70-meter antenna. While any one of the antennas is more than powerful enough to transmit to Voyager, a single 34-meter antenna does not collect enough electromagnetic radiation to detect Voyagers downlink. Antennas at each site can be linked to simultaneously receive the signal from the spacecraft, providing increased gain through radio interferometry.
##### Voyager 2 antenna tracking schedule for Canberra, Australia (click for larger) shows the large 70-meter antenna on the top row and the 34-meter antennas in the bottom three rows. Multiple antennas can be linked to increase gain. Credit: Mark Hughes
Accurately locating the spacecraft on its journey was accomplished with Doppler rangefinding, and later with Very Long Baseline Interferometry (VLBI) along two baselines that extend from Goldstone, California to Madrid, Spain, and from Goldstone, California to Canberra, Australia.
The Goldstone-Madrid baseline is used to determine right-ascension of a spacecraft and the Goldstone-Canberra baseline provides a mix between right-ascension and declination. When combined, the data can locate the spacecraft extremely accurately in the celestial sphere with angular measurement error measured in nano-radians (one nano-radian of error at 1 million kilometers is 100 cm).
### Technical Details
The following technical details of Voyager communication are provided in Deep Space Communication and Navigation Series (Chapter 3), and JPL DESCANSO Volume 4—Voyager Telecommunications.
Each Deep Space Network site has a highly accurate frequency source that can be tuned to compensate for the Doppler frequency shift caused by relative movement between the transmitting and receiving antennas. Compensation takes into account the movement of the spacecraft, the rotation of the Earth around the sun, and the revolution of the Earth around its axis. Receivers are able to detect frequency shifts that are a fraction of a hertz.
The uplink carrier frequency of Voyager 1 is 2114.676697 MHz and 2113.312500 MHz for Voyager 2. The uplink carrier can be modulated with command and/or ranging data. Commands are 16-bps, Manchester-encoded, biphase-modulated onto a 512 HZ square wave subcarrier.
##### Manchester encoding (X0R) illustrated with a blue clock signal, orange data signal, and green result. Credit: Mark Hughes
Voyager's receivers phase lock to the uplink carrier to provide a two-way coherent downlink carrier signal or can use an internal frequency source to produce a non-coherent downlink carrier. The spacecraft can return information to Earth with X-band or S-band transmitters
Voyager 1 2296.481481 2295.000000
8420.432097 8415.000000
Voyager 2 2295.000000 2296.481481
8415.000000 8420.432097
### Conclusion
The Voyager spacecraft will continue their journey for unknown millennia, but we will only be able to communicate with them for another eight years—by that time, the Radionucleotide Thermoelectric Generators will have depleted to the point that they can no longer power Voyager's remaining scientific instruments and transmitters. The spacecraft will fall silent.
Scientists at the Deep Space Network will track the downlink signal from the spacecraft as it sputters into silence and becomes part of the background noise of the solar system—never to be heard from by humans again.
• Kiers 2017-11-19
fascinating!
1) So do the satellites slow down their clock rate the further they are from the sun?
2) Do they use redundant communications (repeating the message)? How many repeats per message string?
3) The chart above indicates around 100Kbps for Galileo and Voyager missions’ bitrate; is that a GROSS bitrate (raw signal) or effective bitrate (after accounting for (subtracting) redundancy)? I’m guessing it’s gross?
• Mark Hughes 2017-11-22
Hi @Kiers,
1) The internal clock rate of the Voyager spacecraft is constant. The Radioisotope Thermonuclear Generators are used to power an alternating current source that is fed to each of the subsystems. The subsystems rectify the signal for power and use the frequency to act as a master clock signal. The communication baud rate (number of clock-signals per logic-level) does decrease with distance.
2) I’m not entirely certain—the answer can likely be found in the Descano reference shown above and if I recall correctly, at some point in the mission, they changed the data encoding algorithm mid-mission, which might change the answer to the question. There is a mild amount of error-correction built into the Manchester code that can be further amplified on the receiving end to detect and correct receiver errors (there will always be one transition per bit—so you’d have to have trouble with several bits in a row to not be able to recover from an error.) Remember too that the Deep Space Network has some of the best receivers on Earth that aren’t subject to the thermal noise most engineers have to deal with—so they might have different assumptions about error than you and I have.
3) The answer here depends on the answer above. If I had to guess, I’d say gross. But it is a guess—it’s been too long since I read the Descano series to give you an affirmative answer.
Best,
Mark
• Jockguy2008 2019-07-17
I can barely make toast in the morning and yet some people are so smart they can figure out how to communicate with spacecraft in the far reaches of space.
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2019-10-18 16:19:09
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http://theinfolist.com/html/ALL/s/Contour_line.html
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TheInfoList
A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a
curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line (geometry), line, but that does not have to be Linearity, straight. Intuitively, a curve may be thought of as the trace left by a moving point (geo ...
along which the function has a constant value, so that the curve joins points of equal value. It is a of the
three-dimensional graphA three-dimensional graph may refer to * A graph (discrete mathematics) In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), spa ...
of the function $f\left(x,y\right)$ parallel to the $\left(x,y\right)$-plane. More generally, a contour line for a function of two variables is a curve connecting points where the function has the same particular value. In
cartography Cartography (; from χάρτης ''chartēs'', "papyrus, sheet of paper, map"; and γράφειν ''graphein'', "write") is the study and practice of making and using s. Combining , , and technique, cartography builds on the premise that rea ...
, a contour line (often just called a "contour") joins points of equal
elevation The elevation of a geographic Geography (from Greek: , ''geographia'', literally "earth description") is a field of science Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scientific ...
(height) above a given level, such as
mean sea level There are several kinds of mean in mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and thei ...
. A contour map is a
map A map is a symbol A symbol is a mark, sign, or that indicates, signifies, or is understood as representing an , , or . Symbols allow people to go beyond what is n or seen by creating linkages between otherwise very different s and s. A ...
illustrated with contour lines, for example a
topographic map Topography concerns the shape and character of the Earth's surface, and maps were among the first artifacts to record these observations. In modern mapping, a topographic map or topographic sheet is a type of map characterized by large- scale ...
, which thus shows valleys and hills, and the steepness or gentleness of slopes. The contour interval of a contour map is the difference in elevation between successive contour lines. The
gradient In vector calculus, the gradient of a scalar-valued function, scalar-valued differentiable function of Function of several variables, several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the Vec ...
of the function is always perpendicular to the contour lines. When the lines are close together the magnitude of the gradient is large: the variation is steep. A
level set In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis ...
is a generalization of a contour line for functions of any number of variables. Contour lines are curved, straight or a mixture of both lines on a
map A map is a symbol A symbol is a mark, sign, or that indicates, signifies, or is understood as representing an , , or . Symbols allow people to go beyond what is n or seen by creating linkages between otherwise very different s and s. A ...
describing the intersection of a real or hypothetical surface with one or more horizontal planes. The configuration of these contours allows map readers to infer the relative gradient of a parameter and estimate that parameter at specific places. Contour lines may be either traced on a visible three-dimensional model of the
surface File:Water droplet lying on a damask.jpg, Water droplet lying on a damask. Surface tension is high enough to prevent floating below the textile. A surface, as the term is most generally used, is the outermost or uppermost layer of a physical obje ...
, as when a photogrammetrist viewing a stereo-model plots elevation contours, or interpolated from the estimated surface
elevations The elevation of a geographic location (geography), location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational equipotential surfa ...
, as when a computer program threads contours through a network of observation points of area centroids. In the latter case, the method of
interpolation In the mathematical Mathematics (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its populatio ...
affects the reliability of individual isolines and their portrayal of
slope In mathematics, the slope or gradient of a line Line, lines, The Line, or LINE may refer to: Arts, entertainment, and media Films * ''Lines'' (film), a 2016 Greek film * ''The Line'' (2017 film) * ''The Line'' (2009 film) * ''The Line'', a ...
, pits and peaks.
# History
The idea of lines that join points of equal value was rediscovered several times. The oldest known
isobath Bathymetry (pronounced ) is the study of underwater depth of ocean floors or lake floors. In other words, bathymetry is the underwater equivalent to hypsometry Hypsometry (from Greek ὕψος, ''hupsos'', "height" and μέτρον, ''metron ...
(contour line of constant depth) is found on a map dated 1584 of the river
Spaarne The Spaarne is a river in North Holland, Netherlands. This partially River engineering#Canalization of rivers, canalized river connects the Ringvaart to a side branch of the North Sea Canal. It runs through Haarlem, Heemstede, and Spaarndam. The hi ...
, near
Haarlem Haarlem (; predecessor of ''Harlem'' in ) is a and in the . It is the of the of . Haarlem is situated at the northern edge of the , one of the s in Europe; it is also part of the . Haarlem had a population of in . Haarlem was granted cit ...
, by Dutchman Pieter Bruinsz. In 1701,
Edmond Halley Edmond (or Edmund) Halley (; – ) was an English astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such ...
used such lines (isogons) on a chart of magnetic variation. The Dutch engineer Nicholas Cruquius drew the bed of the river
Merwede The Merwede (etymology uncertain, possibly derived from the ancient Dutch language, Dutch ''Merwe'' or ''Merowe'', a word meaning "wide water") is the name of several connected stretches of river in the Netherlands, between the cities of Woudrichem, ...
with lines of equal depth (isobaths) at intervals of 1
fathom A fathom is a unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatrical presentation M ...
in 1727, and
Philippe Buache ("Fou-Sang des Chinois", "Fusang of the Chinese") north of the State of California. Image:Fernando de Noronha map by Philippe Buache 1737.jpg, 300px, Philippe Buache,'' Carte d'une partie de l'Océan vers l'Équateur entre les costes d'Afrique et d' ...
used them at 10-fathom intervals on a chart of the
English Channel The English Channel,, "The Sleeve"; nrf, la Maunche, "The Sleeve" (Cotentinais Cotentinais is the dialect The term dialect (from Latin , , from the Ancient Greek word , , "discourse", from , , "through" and , , "I speak") is used in two ...
that was prepared in 1737 and published in 1752. Such lines were used to describe a land surface (contour lines) in a map of the
Duchy of Modena and Reggio The Duchy of Modena and Reggio ( it, Ducato di Modena e Reggio, la, Ducatus Mutinae et Regii) was a small northwestern Italian state that existed from 1452 to 1859, with a break during the Napoleonic Wars The Napoleonic Wars (1803–1815) we ...
by Domenico Vandelli in 1746, and they were studied theoretically by Ducarla in 1771, and
Charles Hutton Charles Hutton FRS FRS may also refer to: Government and politics * Facility Registry System, a centrally managed Environmental Protection Agency database that identifies places of environmental interest in the United States * Family Resourc ...
used them in the
Schiehallion experiment The Schiehallion experiment was an 18th-century experiment An experiment is a procedure carried out to support, refute, or validate a hypothesis. Experiments provide insight into Causality, cause-and-effect by demonstrating what outcome occ ...
. In 1791, a map of France by J. L. Dupain-Triel used contour lines at 20-metre intervals, hachures, spot-heights and a vertical section. In 1801, the chief of the French Corps of Engineers, Haxo, used contour lines at the larger scale of 1:500 on a plan of his projects for Rocca d'Anfo, now in northern Italy, under
Napoleon Napoléon Bonaparte (15 August 1769 – 5 May 1821) was a French military and political leader. He rose to prominence during the French Revolution The French Revolution ( ) refers to the period that began with the Estates General o ...
.R. A. Skelton, "Cartography", ''History of Technology'', Oxford, vol. 6, pp. 612–614, 1958. By around 1843, when the
Ordnance Survey , nativename_a = , nativename_r = , logo = Ordnance Survey 2015 Logo.svg , logo_width = 240px , logo_caption = , seal = , seal_width = , seal_caption = , picture = , picture_width = , picture_caption = , formed = , preceding1 = , di ...
started to regularly record contour lines in
Great Britain Great Britain is an island in the North Atlantic Ocean off the northwest coast of continental Europe. With an area of , it is the largest of the British Isles, the List of European islands by area, largest European island, and the List of i ...
and
Ireland Ireland ( ; ga, Éire ; Ulster Scots dialect, Ulster-Scots: ) is an island in the Atlantic Ocean, North Atlantic. It is separated from Great Britain to its east by the North Channel (Great Britain and Ireland), North Channel, the Irish Sea ...
, they were already in general use in European countries. Isobaths were not routinely used on
nautical chart A nautical chart is a graphic representation of a sea area and adjacent coastal regions. Depending on the scale (map), scale of the chart, it may show depths of water and heights of land (topographic map), natural features of the seabed, details ...
s until those of
Russia Russia ( rus, link=no, Россия, Rossiya, ), or the Russian Federation, is a country spanning Eastern Europe Eastern Europe is the eastern region of . There is no consistent definition of the precise area it covers, partly because th ...
from 1834, and those of Britain from 1838. As different uses of the technique were invented independently, cartographers began to recognize a common theme, and debated what to call these "lines of equal value" generally. The word ''isogram'' ( grc , ἴσος, isos, equal + grc, γράμμα, gramma, writing or drawing) was proposed by
Francis Galton Sir Francis Galton, FRS FRS may also refer to: Government and politics * Facility Registry System, a centrally managed Environmental Protection Agency database that identifies places of environmental interest in the United States * Family Re ...
in 1889 for lines indicating equality of some physical condition or quantity, though ''isogram'' can also refer to a word without a repeated letter. As late as 1944, John K. Wright still preferred ''isogram'', but it never attained wide usage. During the early 20th Century, ''isopleth'' ( grc, πλῆθος, plethos, amount) was being used by 1911 in the United States, while ''isarithm'' ( grc, ἀριθμός, arithmos, number) had become common in Europe. Additional alternatives, including the Greek-English hybrid ''isoline'' and ''isometric line'' ( grc, μέτρον, metron, measure), also emerged. Despite attempts to select a single standard, all of these alternatives have survived to the present. When maps with contour lines became common, the idea spread to other applications. Perhaps the latest to develop are
air quality Air pollution is the presence of substances in the atmosphere An atmosphere (from the greek words ἀτμός ''(atmos)'', meaning 'vapour', and σφαῖρα ''(sphaira)'', meaning 'ball' or 'sphere') is a layer or a set of layers of gas ...
and
noise pollution Noise pollution, also known as or sound , is the propagation of noise with ranging impacts on the activity of human or animal life, most of them harmful to a degree. The source of outdoor noise worldwide is mainly caused by machines, transport, ...
contour maps, which first appeared in the United States in approximately 1970, largely as a result of national legislation requiring spatial delineation of these parameters.
# Types
Contour lines are often given specific names beginning "iso-" ( grc, ἴσος, isos, equal) according to the nature of the variable being mapped, although in many usages the phrase "contour line" is most commonly used. Specific names are most common in meteorology, where multiple maps with different variables may be viewed simultaneously. The prefix "iso-" can be replaced with "isallo-" to specify a contour line connecting points where a variable changes at the same ''rate'' during a given time period. An isogon (from or ''gonia'', meaning 'angle') is a contour line for a variable which measures direction. In meteorology and in geomagnetics, the term ''isogon'' has specific meanings which are described below. An isocline (from or ''klinein'', meaning 'to lean or slope') is a line joining points with equal slope. In population dynamics and in geomagnetics, the terms ''isocline'' and ''isoclinic line'' have specific meanings which are described below.
## Equidistant points
A curve of equidistant points is a set of points all at the same distance from a given
point Point or points may refer to: Places * Point, LewisImage:Point Western Isles NASA World Wind.png, Satellite image of Point Point ( gd, An Rubha), also known as the Eye Peninsula, is a peninsula some 11 km long in the Outer Hebrides (or Western I ...
,
line Line, lines, The Line, or LINE may refer to: Arts, entertainment, and media Films * ''Lines'' (film), a 2016 Greek film * ''The Line'' (2017 film) * ''The Line'' (2009 film) * ''The Line'', a 2009 independent film by Nancy Schwartzman Lite ...
, or polyline. In this case the function whose value is being held constant along a contour line is a
distance function In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no ge ...
.
## Isopleths
In 1944, John K. Wright proposed that the term ''isopleth'' be used for contour lines that depict a variable which cannot be measured at a point, but which instead must be calculated from data collected over an area, as opposed to ''isometric lines'' for variables that could be measured at a point; this distinction has since been followed generally. An example of an isopleth is
population density Population density (in agriculture: Stock (disambiguation), standing stock or plant density) is a measurement of population per unit area, or exceptionally unit volume; it is a quantity of type number density. It is frequently applied to livin ...
, which can be calculated by dividing the population of a census district by the surface area of that district. Each calculated value is presumed to be the value of the variable at the centre of the area, and isopleths can then be drawn by a process of
interpolation In the mathematical Mathematics (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its populatio ...
. The idea of an isopleth map can be compared with that of a
choropleth map A choropleth map () is a type of thematic map in which a set of pre-defined areas is colored or patterned in proportion to a statistical variable that represents an aggregate summary of a geographic characteristic within each area, such as pop ...
. In meteorology, the word ''isopleth'' is used for any type of contour line.
## Meteorology
Meteorological contour lines are based on
interpolation In the mathematical Mathematics (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its populatio ...
of the point data received from
weather stationyumyum, Victoria, Australia Australia, officially the Commonwealth of Australia, is a Sovereign state, sovereign country comprising the mainland of the Australia (continent), Australian continent, the island of Tasmania, and numerous List o ...
s and
weather satellite A weather is a type of that is primarily used to monitor the and of the Earth. Satellites can be ing (covering the entire Earth asynchronously), or (hovering over the same spot on the ). While primarily used to detect the development and m ...
s. Weather stations are seldom exactly positioned at a contour line (when they are, this indicates a measurement precisely equal to the value of the contour). Instead, lines are drawn to best approximate the locations of exact values, based on the scattered information points available. Meteorological contour maps may present collected data such as actual air pressure at a given time, or generalized data such as average pressure over a period of time, or forecast data such as predicted air pressure at some point in the future.
Thermodynamic diagrams Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
use multiple overlapping contour sets (including isobars and isotherms) to present a picture of the major thermodynamic factors in a weather system.
### Barometric pressure
An isobar (from or ''baros'', meaning 'weight') is a line of equal or constant
pressure Pressure (symbol: ''p'' or ''P'') is the force In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space ...
on a graph, plot, or map; an isopleth or contour line of pressure. More accurately, isobars are lines drawn on a map joining places of equal average atmospheric pressure reduced to sea level for a specified period of time. In
meteorology Meteorology is a branch of the (which include and ), with a major focus on . The study of meteorology dates back , though significant progress in meteorology did not begin until the 18th century. The 19th century saw modest progress in the f ...
, the
barometric pressure Atmospheric pressure, also known as barometric pressure (after the barometer), is the pressure within the atmosphere of Earth File:Atmosphere gas proportions.svg, Composition of Earth's atmosphere by volume, excluding water vapor. Lower pie ...
s shown are reduced to
sea level Mean sea level (MSL) (often shortened to sea level) is an average In colloquial, ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in th ...
, not the surface pressures at the map locations. The distribution of isobars is closely related to the magnitude and direction of the
wind Wind is the natural movement of air or other gases relative to a planet's surface. Wind occurs on a range of scales, from thunderstorm A thunderstorm, also known as an electrical storm or a lightning storm, is a storm characterized by th ...
field, and can be used to predict future weather patterns. Isobars are commonly used in television weather reporting. Isallobars are lines joining points of equal pressure change during a specific time interval. These can be divided into ''anallobars'', lines joining points of equal pressure increase during a specific time interval, and ''katallobars'', lines joining points of equal pressure decrease. In general, weather systems move along an axis joining high and low isallobaric centers. Isallobaric gradients are important components of the wind as they increase or decrease the
geostrophic wind In atmospheric science Atmospheric science is the study of the Earth's atmosphere and its various inner-working physical processes. Meteorology Meteorology is a branch of the atmospheric sciences which includes atmospheric chemistry and a ...
. An isopycnal is a line of constant density. An ''isoheight'' or ''isohypse'' is a line of constant
geopotential Geopotential is the potential of the Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. About 29% of Earth's surface is land consisting of continent A continent is one of several la ...
height on a constant pressure surface chart. Isohypse and isoheight are simply known as lines showing equal pressure on a map.
### Temperature and related subjects
An isotherm (from or ''thermē'', meaning 'heat') is a line that connects points on a map that have the same
temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concept ...
. Therefore, all points through which an isotherm passes have the same or equal temperatures at the time indicated. An isotherm at 0 °C is called the freezing level. The term was coined by the
Prussia Prussia, , Old Prussian Distribution of the Baltic tribes, circa 1200 CE (boundaries are approximate). Old Prussian was a Western Baltic language belonging to the Balto-Slavic branch of the Indo-European languages The Indo-Europ ...
n geographer and naturalist
Alexander von Humboldt Friedrich Wilhelm Heinrich Alexander von Humboldt (14 September 17696 May 1859) was a , , , , and proponent of philosophy and . He was the younger brother of the Prussian minister, philosopher, and (1767–1835). Humboldt's quantitative work ...
, who as part of his research into the geographical distribution of plants published the first map of isotherms in Paris, in 1817. An isocheim is a line of equal mean winter temperature, and an isothere is a line of equal mean summer temperature. An isohel (from or ''helios'', meaning 'Sun') is a line of equal or constant
solar radiation Solar irradiance is the power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one j ...
. An isogeotherm is a line of equal temperature beneath the Earth's surface.
### Rainfall and air moisture
An isohyet or isohyetal line (from or , meaning 'rain') is a line joining points of equal rainfall on a
map A map is a symbol A symbol is a mark, sign, or that indicates, signifies, or is understood as representing an , , or . Symbols allow people to go beyond what is n or seen by creating linkages between otherwise very different s and s. A ...
in a given period. A map with isohyets is called an isohyetal map. An isohume is a line of constant relative
humidity Humidity is the concentration of water vapour (99.9839 °C) , - , Boiling point , , - , specific gas constant , 461.5 J/( kg·K) , - , Heat of vaporization , 2.27 MJ/kg , - , Heat capacity , 1.864 kJ/(kg·K) Water vapo ...
, while an isodrosotherm (from or ''drosos'', meaning 'dew', and or ''therme'', meaning 'heat') is a line of equal or constant
dew point Warmer air can hold more moisture than colder air. The dew point is the temperature to which air must be cooled to become saturated with water vapor. It is assumed that air pressure and water content is constant. When cooled further, the air ...
. An isoneph is a line indicating equal
cloud In meteorology, a cloud is an aerosol consisting of a visible mass of minute liquid drop (liquid), droplets, ice crystals, frozen crystals, or other particulates, particles suspended in the atmosphere of a planetary body or similar space. Wate ...
cover. An isochalaz is a line of constant frequency of
hail Hail is a form of solid precipitation In meteorology Meteorology is a branch of the atmospheric sciences Atmospheric science is the study of the Earth's atmosphere File:Atmosphere gas proportions.svg, Composition of Earth's atmo ...
storms, and an isobront is a line drawn through geographical points at which a given phase of thunderstorm activity occurred simultaneously.
Snow Snow comprises individual ice Ice is water Water (chemical formula H2O) is an , transparent, tasteless, odorless, and , which is the main constituent of 's and the s of all known living organisms (in which it acts as a ). ...
cover is frequently shown as a contour-line map.
### Wind
An isotach (from or , meaning 'fast') is a line joining points with constant
wind Wind is the natural movement of air or other gases relative to a planet's surface. Wind occurs on a range of scales, from thunderstorm A thunderstorm, also known as an electrical storm or a lightning storm, is a storm characterized by th ...
speed. In meteorology, the term isogon refers to a line of constant wind direction.
### Freeze and thaw
An isopectic line denotes equal dates of
ice Ice is water Water (chemical formula H2O) is an , transparent, tasteless, odorless, and , which is the main constituent of 's and the s of all known living organisms (in which it acts as a ). It is vital for all known forms of , eve ...
formation each winter, and an isotac denotes equal dates of thawing.
## Physical geography and oceanography
### Elevation and depth
Contours are one of several common methods used to denote
elevation The elevation of a geographic Geography (from Greek: , ''geographia'', literally "earth description") is a field of science Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scientific ...
or
altitude Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference and a point or object. The exact definition and reference datum varies according to the context (e.g. ...
and depth on
map A map is a symbol A symbol is a mark, sign, or that indicates, signifies, or is understood as representing an , , or . Symbols allow people to go beyond what is n or seen by creating linkages between otherwise very different s and s. A ...
s. From these contours, a sense of the general
terrain Relief map of Sierra Nevada, Spain Terrain or relief (also topographical Topography is the study of the forms and features of land surfaces. The topography of an area could refer to the surface forms and features themselves, or a desc ...
can be determined. They are used at a variety of scales, from large-scale engineering drawings and architectural plans, through
topographic maps Topography Topography is the study of the forms and features of land surfaces. The topography of an area could refer to the surface forms and features themselves, or a description (especially their depiction in maps). Topography is a fiel ...
and bathymetric charts, up to continental-scale maps. "Contour line" is the most common usage in
cartography Cartography (; from χάρτης ''chartēs'', "papyrus, sheet of paper, map"; and γράφειν ''graphein'', "write") is the study and practice of making and using s. Combining , , and technique, cartography builds on the premise that rea ...
, but
isobath Bathymetry (pronounced ) is the study of underwater depth of ocean floors or lake floors. In other words, bathymetry is the underwater equivalent to hypsometry Hypsometry (from Greek ὕψος, ''hupsos'', "height" and μέτρον, ''metron ...
for underwater depths on
bathymetric Bathymetry (pronounced ) is the study of underwater depth of ocean floors or lake floors. In other words, bathymetry is the underwater equivalent to hypsometry or topography. The name comes from Greek language, Greek βαθύς (''bathus''), "deep ...
maps and isohypse for elevations are also used. In cartography, the contour interval is the elevation difference between adjacent contour lines. The contour interval should be the same over a single map. When calculated as a ratio against the map scale, a sense of the hilliness of the terrain can be derived.
### = Interpretation
= There are several rules to note when interpreting terrain contour lines: * The rule of Vs: sharp-pointed vees usually are in stream valleys, with the drainage channel passing through the point of the vee, with the vee pointing upstream. This is a consequence of
erosion In earth science Earth science or geoscience includes all fields of natural science Natural science is a branch of science Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scientific ...
. * The rule of Os: closed loops are normally uphill on the inside and downhill on the outside, and the innermost loop is the highest area. If a loop instead represents a depression, some maps note this by short lines called hachures which are perpendicular to the contour and point in the direction of the low. (The concept is similar to but distinct from hachures used in hachure maps.) * Spacing of contours: close contours indicate a steep slope; distant contours a shallow slope. Two or more contour lines merging indicates a cliff. By counting the number of contours that cross a segment of a
stream A stream is a body of water (Lysefjord) in Norway Norway, officially the Kingdom of Norway,Names in the official and recognised languages: Bokmål Bokmål (, ; literally "book tongue") is an official written standard for the No ...
, the
stream gradientStream gradient is the grade (slope), grade measured by the ratio of drop in elevation of a stream per unit horizontal distance, usually expressed as metre, meters per kilometre, kilometer or Foot (length), feet per mile. Hydrology and geology A hig ...
can be approximated. Of course, to determine differences in elevation between two points, the contour interval, or distance in altitude between two adjacent contour lines, must be known, and this is normally stated in the map key. Usually contour intervals are consistent throughout a map, but there are exceptions. Sometimes intermediate contours are present in flatter areas; these can be dashed or dotted lines at half the noted contour interval. When contours are used with hypsometric tints on a small-scale map that includes mountains and flatter low-lying areas, it is common to have smaller intervals at lower elevations so that detail is shown in all areas. Conversely, for an island which consists of a plateau surrounded by steep cliffs, it is possible to use smaller intervals as the height increases.
### Electrostatics
An isopotential map is a measure of electrostatic potential in space, often depicted in two dimensions with the electrostatic charges inducing that
electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work Work may refer to: * Work (human activity), intentional activity people perform to support the ...
. The term
equipotential Equipotential or isopotential in mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathema ...
line or isopotential line refers to a curve of constant
electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work Work may refer to: * Work (human activity), intentional activity people perform to support the ...
. Whether crossing an equipotential line represents ascending or descending the potential is inferred from the labels on the charges. In three dimensions,
equipotential Equipotential or isopotential in mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathema ...
surfaces may be depicted with a two dimensional cross-section, showing
equipotential Equipotential or isopotential in mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathema ...
lines at the intersection of the surfaces and the cross-section. The general mathematical term
level set In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis ...
is often used to describe the full collection of points having a particular potential, especially in higher dimensional space.
### Magnetism
In the study of the
Earth's magnetic field Earth's magnetic field, also known as the geomagnetic field, is the magnetic field A magnetic field is a vector field In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space. Fo ...
, the term isogon or isogonic line refers to a line of constant
magnetic declination #REDIRECT Magnetic declination Magnetic declination, or magnetic variation, is the angle on the horizontal plane between magnetic north (the direction the north end of a magnetized compass needle points, corresponding to the direction of the Ear ...
, the variation of magnetic north from geographic north. An agonic line is drawn through points of zero magnetic declination. An isoporic line refers to a line of constant annual variation of magnetic declination . An isoclinic line connects points of equal
magnetic dip upIllustration of magnetic dip from Norman's book, ''The Newe Attractive'' Magnetic dip, dip angle, or magnetic inclination is the angle made with the horizontal by the Earth's magnetic field lines. This angle varies at different points on the Ear ...
, and an aclinic line is the isoclinic line of magnetic dip zero. An isodynamic line (from or ''dynamis'' meaning 'power') connects points with the same intensity of magnetic force.
### Oceanography
Besides ocean depth,
oceanographers Oceanography (compound of the Greek language, Greek words ὠκεανός meaning "ocean" and γράφω meaning "Writing, write"), also known as oceanology, is the study of the physical and biological aspects of the ocean. It is an important Ea ...
use contour to describe diffuse variable phenomena much as meteorologists do with atmospheric phenomena. In particular, isobathytherms are lines showing depths of water with equal temperature, isohalines show lines of equal ocean salinity, and isopycnals are surfaces of equal water density.
## Geology
Various
geological Geology (from the Ancient Greek γῆ, ''gē'' ("earth") and -λoγία, ''-logia'', ("study of", "discourse")) is an Earth science concerned with the solid Earth, the rock (geology), rocks of which it is composed, and the processes by which th ...
data are rendered as contour maps in
structural geology Structural geology is the study of the three-dimensional distribution of rock Rock most often refers to: * Rock (geology) A rock is any naturally occurring solid mass or aggregate of minerals or mineraloid matter. It is categorized by th ...
,
sedimentology Sedimentology encompasses the study of modern sediment Sediment is a naturally occurring material that is broken down by processes of weathering Weathering is the deterioration of rocks A rock is any naturally occurring solid mass o ...
,
stratigraphy Stratigraphy is a branch of geology concerned with the study of rock (geology), rock layers (Stratum, strata) and layering (stratification). It is primarily used in the study of sedimentary rock, sedimentary and layered volcanic rocks. Stratigrap ...
and
economic geology Economic geology is concerned with earth materials that can be used for economic and/or industrial purposes. These materials include precious and base metals, nonmetallic minerals and construction-grade stone. Economic geology is a subdisciplin ...
. Contour maps are used to show the below ground surface of geologic
strata (Argentina Argentina (), officially the Argentine Republic ( es, link=no, República Argentina), is a country located mostly in the southern half of South America. Sharing the bulk of the Southern Cone with Chile to the west, the country is a ...
,
fault Fault commonly refers to: *Fault (geology), planar rock fractures showing evidence of relative movement *Fault (law), blameworthiness or responsibility Fault(s) may also refer to: Arts, entertainment, and media * "Fault", a song by Taproot from ...
surfaces (especially low angle
thrust fault , Somerset, England; displacement of about A thrust fault is a break in the Earth's crust, across which older rocks are pushed above younger rocks. Thrust geometry and nomenclature File:Fault-propagation fold.gif, 150px, Diagram of the evolut ...
s) and
unconformities An unconformity is a buried erosional or non-depositional surface separating two rock masses or strata (Argentina Argentina (), officially the Argentine Republic ( es, link=no, República Argentina), is a country located mostly in the sout ...
.
Isopach map An isopach map () illustrates thickness variations within a tabular unit, layer or stratum. Isopachs are contour lines of equal thickness over an area. Isopach maps are utilized in hydrographic survey, stratigraphy, sedimentology, structural geolog ...
s use isopachs (lines of equal thickness) to illustrate variations in thickness of geologic units.
## Environmental science
In discussing pollution, density maps can be very useful in indicating sources and areas of greatest contamination. Contour maps are especially useful for diffuse forms or scales of pollution. Acid precipitation is indicated on maps with isoplats. Some of the most widespread applications of environmental science contour maps involve mapping of
environmental noise Environmental noise is an accumulation of noise pollution that occurs outside. This noise can be caused by transport, industrial, and Sport, recreational activities. Noise is frequently described as 'unwanted sound'. Within this context, environ ...
(where lines of equal sound pressure level are denoted isobels),
air pollution Air pollution is the presence of substances in the atmosphere that are harmful to the health of humans and other Outline of life forms, living beings, or cause damage to the climate or to materials. There are different types of air pollutants, ...
,
soil contamination 280px, Excavation showing soil contamination at a disused gasworks in England. Soil contamination or soil pollution as part of land degradation is caused by the presence of xenobiotics (human-made) chemicals or other alteration in the natural soil ...
,
thermal pollution Thermal pollution, sometimes called "thermal enrichment," is the degradation of water quality by any process that changes ambient water temperature Temperature is a physical quantity that expresses hot and cold. It is the manifestation of ...
and
groundwater Groundwater is the water Water (chemical formula H2O) is an , transparent, tasteless, odorless, and , which is the main constituent of 's and the s of all known living organisms (in which it acts as a ). It is vital for all known form ...
contamination. By contour planting and contour ploughing, the rate of water runoff and thus soil erosion can be substantially reduced; this is especially important in riparian zones.
## Ecology
An isoflor is an isopleth contour connecting areas of comparable biological diversity. Usually, the variable is the number of species of a given genus or family that occurs in a region. Isoflor maps are thus used to show distribution patterns and trends such as centres of diversity.
## Social sciences
In economics, contour lines can be used to describe features which vary quantitatively over space. An wikt:isochrone, isochrone shows lines of equivalent drive time or travel time to a given location and is used in the generation of isochrone maps. An isotim shows equivalent transport costs from the source of a raw material, and an isodapane shows equivalent cost of travel time. Contour lines are also used to display non-geographic information in economics. Indifference curves (as shown at left) are used to show bundles of goods to which a person would assign equal utility. An isoquant (in the image at right) is a curve of equal production quantity for alternative combinations of factors of production, input usages, and an isocost, isocost curve (also in the image at right) shows alternative usages having equal production costs. In political science an analogous method is used in understanding coalitions (for example the diagram in Laver and Shepsle's work). In population dynamics, an isocline shows the set of population sizes at which the rate of change, or partial derivative, for one population in a pair of interacting populations is zero.
## Statistics
In statistics, isodensity lines or isodensanes are lines that join points with the same value of a probability density. Isodensanes are used to display bivariate distributions. For example, for a bivariate elliptical distribution the isodensity lines are ellipses.
## Thermodynamics, engineering, and other sciences
Various types of graphs in thermodynamics, engineering, and other sciences use isobars (constant pressure), isotherms (constant temperature), isochors (constant specific volume), or other types of isolines, even though these graphs are usually not related to maps. Such isolines are useful for representing more than two dimensions (or quantities) on two-dimensional graphs. Common examples in thermodynamics are some types of phase diagrams. Isoclines are used to solve ordinary differential equations. In interpreting radar images, an isodop is a line of equal Doppler effect, Doppler velocity, and an isoecho is a line of equal radar reflectivity. In the case of hybrid contours, energies of hybrid orbitals and the energies of pure atomic orbitals are plotted. The graph obtained is called hybrid contour.
## Other phenomena
* ''isochasm'': aurora (astronomy), aurora equal occurrence * ''isochor'': volume * ''isodose'': absorbed dose of radiation * ''isophene'': biological events occurring with coincidence such as plants flowering * ''isophote'': illuminance * mobile telephony: Received signal strength indication, mobile received power and Coverage (telecommunication), cell coverage area
# Algorithms
* finding boundaries of level sets after image segmentation ** Edge detection ** Level-set method ** Boundary tracing * Active contour model
# Graphical design
To maximize readability of contour maps, there are several design choices available to the map creator, principally line weight, line color, line type and method of numerical marking. Line weight is simply the darkness or thickness of the line used. This choice is made based upon the least intrusive form of contours that enable the reader to decipher the background information in the map itself. If there is little or no content on the base map, the contour lines may be drawn with relatively heavy thickness. Also, for many forms of contours such as topographic maps, it is common to vary the line weight and/or color, so that a different line characteristic occurs for certain numerical values. For example, in the topographic map above, the even hundred foot elevations are shown in a different weight from the twenty foot intervals. Line color is the choice of any number of pigments that suit the display. Sometimes a Gloss (paint), sheen or gloss is used as well as color to set the contour lines apart from the base map. Line colour can be varied to show other information. Line type refers to whether the basic contour line is solid, dashed, dotted or broken in some other pattern to create the desired effect. Dotted or dashed lines are often used when the underlying base map conveys very important (or difficult to read) information. Broken line types are used when the location of the contour line is inferred. Numerical marking is the manner of denoting the arithmetical values of contour lines. This can be done by placing numbers along some of the contour lines, typically using
interpolation In the mathematical Mathematics (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its populatio ...
for intervening lines. Alternatively a map key can be produced associating the contours with their values. If the contour lines are not numerically labeled and adjacent lines have the same style (with the same weight, color and type), then the direction of the gradient cannot be determined from the contour lines alone. However, if the contour lines cycle through three or more styles, then the direction of the gradient can be determined from the lines. The orientation of the numerical text labels is often used to indicate the direction of the slope.
# Plan view versus profile view
Most commonly contour lines are drawn in plan view, or as an observer in space would view the Earth's surface: ordinary map form. However, some parameters can often be displayed in profile view showing a vertical profile of the parameter mapped. Some of the most common parameters mapped in profile are air pollutant concentrations and Sound exposure level, sound levels. In each of those cases it may be important to analyze (air pollutant concentrations or sound levels) at varying heights so as to determine the air quality or noise health effects on people at different elevations, for example, living on different floor levels of an urban apartment. In actuality, both plan and profile view contour maps are used in
air pollution Air pollution is the presence of substances in the atmosphere that are harmful to the health of humans and other Outline of life forms, living beings, or cause damage to the climate or to materials. There are different types of air pollutants, ...
and
noise pollution Noise pollution, also known as or sound , is the propagation of noise with ranging impacts on the activity of human or animal life, most of them harmful to a degree. The source of outdoor noise worldwide is mainly caused by machines, transport, ...
studies.
# Labeling contour maps
Labeling (map design), Labels are a critical component of elevation maps. A properly labeled contour map helps the reader to quickly interpret the shape of the terrain. If numbers are placed close to each other, it means that the terrain is steep. Labels should be placed along a slightly curved line "pointing" to the summit or nadir, from several directions if possible, making the visual identification of the summit or nadir easy.Freeman, H., "Computer Name Placement," ch. 29, in Geographical Information Systems, 1, D.J. Maguire, M.F. Goodchild, and D.W. Rhind, John Wiley, New York, 1991, 449–460. Contour labels can be oriented so a reader is facing uphill when reading the label. Manual labeling of contour maps is a time-consuming process, however, there are a few software systems that can do the job automatically and in accordance with cartographic conventions, called automatic label placement.
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2022-08-11 18:17:19
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http://mathhelpforum.com/algebra/30575-factorizing-ehh.html
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# Math Help - factorizing ehh :(
1. ## factorizing ehh :(
hey guys, just doin a lil study..im a little confused about these questions.
factor these two questions:
1)
$
81x^2 - 16y^2
$
2)
$
(y+3)^3 + 8
$
any ideas?
2. 1. This is a product of 2 squares .
$
81x^2 - 16y^2 = (9x - 4y)(9x + 4y)
$
2. Multiply out the brackets and add the 8. Then factorise:
$
(y+3)^3 + 8 = y^3 + 9y^2 + 27y + 35 = (y+5)(y^2+4y+7)
$
Hope this helps.
3. Considering that you seem to be focusing on difference of squares, sum and difference of cubes, the intention is probably, for #2, that you recognize that $(y+3)^3 + 8$ is a difference of cubes and use that formula (where $a = (y + 3), b = 2$). You can do it the other way - multiply it all out - as well.
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2016-06-25 13:42:06
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https://encyclopediaofmath.org/wiki/Poisson_manifold
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Poisson manifold
Poisson manifold
A Poisson bracket on a smooth manifold $M$ is a Lie bracket $\{~,~\}$ on the space of smooth functions $C^\infty(M)$ which, additionally, satisfies the Leibniz identity: $$\{f,gh\}=\{f,g\}h+g\{f,h\},\qquad \forall f,g,h\in C^\infty(M).$$ The pair $(M,\{~,~\})$ is called a Poisson manifold. A smooth map between Poisson manifolds $\phi:(M,\{~,~\}_M)\to (N,\{~,~\}_N)$ such that the induced pullback map $\phi^*:C^\infty(N)\to C^\infty(M)$ is a Lie algebra morphism is called a Poisson map.
Examples of Poisson manifolds
Examples of Poisson manifolds include symplectic manifolds and linear Poisson structures.
Symplectic manifolds
If $(S,\omega)$ is any symplectic manifold and $f\in C^\infty(M)$ is a smooth function then one defines a vector field $X_f$ on $S$, called the hamiltonian vector field associated to $f$, by setting $$i_{X_f}\omega =\mathrm{d}f.$$ The associated Poisson bracket on $S$ is then given by: $$\{f,g\}(v):=X_f(g)=-X_g(f).$$
Linear Poisson brackets
A Poisson bracket on a vector space $V$ is called a linear Poisson bracket if the Poisson bracket of any two linear functions is again a linear function. Since linear functions form the dual vector space $V^*$ this means that a linear Poisson bracket in $V$ determines a Lie algebra structure on $\mathfrak{g}:=V^*$. Conversely, if $\mathfrak{g}$ is a finite dimensional Lie algebra then its dual vector space $V:=\mathfrak{g}^*$ carries a linear Poisson bracket which is given by the formula: $$\{f,g\}(v):=\langle [\mathrm{d}_v f, \mathrm{d}_v g], v\rangle.$$
Heisenberg Poisson bracket
If $(S,\omega)$ is any symplectic manifold with associated Poisson bracket $\{~,~\}_S$ then one can define a new Poisson bracket on $M:=S\times\mathbb{R}$ by setting: $$\{f,g\}_M(x,t)=\{f(\cdot,t),g(\cdot,t)\}_S(x).$$ This is called the Heisenberg Poisson bracket. Actually the same construction can be performed replacing $S$ by any Poisson manifold.
Hamiltonian Systems and Symmetries
Hamiltonian vector fields
On a Poisson manifold $(M,\{~,~\})$, any smooth function $h\in C^\infty(M)$ determines a hamiltonian vector field $X_h$ by setting: $$X_h(f):=\{h,f\}.$$
One calls the function $h$ the hamiltonian. Note that for a symplectic manifold, viewed as a Poisson manifold, this definition is consistent with the old definition. The flow $\Phi^t_{X_h}$ of a hamiltonian vector field preserves the hamiltonian: $$h\circ \Phi^t_{X_h}=h.$$
On a Poisson manifold $(M,\{~,~\})$, the functions $f\in C^\infty(M)$ for which the hamiltonian vector field $X_f$ vanishes identically are called Casimirs. They form the center of the Lie algebra $(C^\infty(M),\{~,~\})$.
Poisson vector fields
A vector field $X$ on Poisson manifold $(M,\{~,~\})$ is called a Poisson vector field if it is a derivation of the Poisson bracket: $X(\{f,g\})=\{X(f),g\}+\{f,X(g)\}.$ The Jacobi identity shows that any hamiltonian vector field is a Poisson vector field. If $\Phi^t_X$ denotes the flow of the vector field $X$, then $X$ is a Poisson vector field if and only if $\Phi^t_X$ is a 1-paremeter group of Poisson diffeomorphisms.
The vector space $H^1_\pi(M)$ formed by the quotient of the Poisson vector fields modulo hamiltonian vector fields is called the first Poisson cohomology of $M$.
Moment maps
Let $G$ be a Lie group which acts smoothly on a Poisson manifold $(M,\{~,~\})$. We say that $G$ is a symmetry group or that $G\times M \to M$ is a Poisson action iif the action is by Poisson diffeomorphisms. If $G$ is connected and $\rho:\mathfrak{g}\to \mathcal{X}(M)$ is the corresponding infinitesimal action, then the group is a symmetry group if and on if each vector field $\rho(\xi)$ is a Poisson vector field.
A hamiltonian action $G\times M \to M$ is a Poisson action such that the vector fields $\rho(\xi)$ are hamiltonian vector fields: $$\rho(\xi)=X_{\mu^*(\xi)},$$ for some smooth $G$-equivariant map $\mu:M\to \mathfrak{g}^*$. Here $\mu^*:\mathfrak{g}\to C^\infty(M)$ denotes the map $\mu^*(\xi)(x)=\langle \mu(x),\xi\rangle$. One calls $\mu$ the moment map.
Constructions with Poisson manifolds
There are many constructions which produce new Poisson manifolds out of old ones.
Poisson submanifolds
Let $(M,\{~,~\})$ be a Poisson manifold and suppose $N\subset M$ is a submanifold with the property that for any $f\in C^\infty(M)$ the hamiltonian vector field $X_f$ is tangent to $N$. Then we have an induced Poisson bracket on $N$ defined by: $$\{f,g\}_N=\{F,G\}|_N, \forall f,g\in C^\infty(N),$$ where $F,G\in C^\infty(M)$ are any extensions of $f$ and $g$ to $M$: $F|_N=f$ and $G|_N=g$.
Product of Poisson manifolds
If $(M,\{~,~\}_M)$ and $(N,\{~,~\}_N)$ are two Poisson manifolds then their product is the Poisson manifold $(M\times N,\{~,~\}_{M\times N})$ where the Poisson bracket is defined by: $$\{f,g\}_{M\times N}(x,y):=\{f(\cdot,y),g(\cdot,y)\}_M(x)+\{f(x,\cdot),g(x,\cdot)\}_N(y), \qquad \forall (x,y)\in M\times N.$$ This is the unique Poisson bracket for which the projections $\pi_M:M\times N\to M$ and $\pi_N:M\times N\to N$ are Poisson maps.
Poisson quotients
If $(M,\{~,~\}_M)$ is a Poisson manifold and $G\times M\to M$ is a smooth Lie group action by Poisson diffeomorphisms then the Poisson bracket of any two $G$-invariant functions $f,g\in C^\infty(M)^G$ is again a $G$-invariant function: $\{f,g\}\in C^\infty(M)^G$.
When the action is free and proper, $M/G$ is a smooth manifold and $C^\infty(M/G)\equiv C^\infty(M)^G$, so it follows that $M/G$ carries a natural Poisson bracket $\{~,~\}_{M/G}$. It is the unique Poisson bracket for which the quotient map $q:M\to M/G$ is a Poisson map.
References
• A. Cannas da Silva, A. Weinstein, Geometric models for noncommutative algebras, Berkeley Mathematics Lecture Notes, 10. American Mathematical Society, Providence, RI, 1999. ISBN: 0-8218-0952-0
• J.P. Dufour, N.T. Zung, Poisson structures and their normal forms, Progress in Mathematics, 242. Birkhäuser Verlag, Basel, 2005. ISBN: 978-3-7643-7334-4
• A. Lichnerowicz, Les variétés de Poisson et leurs algèbres de Lie associées, J. Diff. Geom. 12 (1977), n. 2, 253–300.
• A. Weinstein, The local structure of Poisson manifolds, J. Diff. Geom. 18 (1983), n.3, 523–557 (Errata and addenda J. Diff. Geom. 22 (1985), 255.)
How to Cite This Entry:
Poisson manifold. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Poisson_manifold&oldid=31053
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2022-08-17 00:55:55
|
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https://ilcctv.com/feste-pronunciation-mwv/69629c-jupyterlab-latex-tutorial
|
The Name Jupyter is a merge of the inital three programming languages Julia Python and R ;JuPyteR Now let us see how… To use, right-click on an open .tex document within JupyterLab, and select Show LaTeX Preview:This will compile the .texfile and open the rendered PDF document.Subsequent saves of the file will automatically update the PDF.If the PDF fails to compile (possibly due to a syntax error),an error panel will open detailing the LaTeX error. Here are my top five unexpected and creative ways to use Jupyter. Some examples from the MathJax demos site are reproduced below, as well as the Markdown+TeX source. JupyterLab is an integrated environment that can streamline the development of Python code and Machine Learning (ML) models in Kinetica. Just put your LaTeX math inside . In order to use it, you must enable both of them. Jupyter Notebook LaTeX example, aligned center. JupyterLab Tutorials Jupyterlab is the next generation jupyter notebook. LaTeX is a JupyterLab extension that lets you live-edit LaTeX … However, it can also be installed separately by using following conda command −, You can also use the pip command for this purpose −. Digging into some JupyterLab with LATEX and creating beatiful reports for end user. To use, right-click on an open .tex document within JupyterLab, and select Show LaTeX Preview: This will compile the .tex file and open the rendered PDF document. Photo by Joshua Sortino on Unsplash. Try it on Binder.JupyterLab follows the Jupyter Community Guides. Many of those were addressed by JupyterLab, with the addition of tabs, extension manager, themes and shortcuts editor.As a heavy JupyterLabs user, I spend 80% of my time … This means that you can freely mix in mathematical expressions using the MathJax subset of Tex and LaTeX. 2. This tutorial is significantly based on the JupyterLab documentation “The JupyterLab Interface” section. Word) before, you can learn LaTeX in no time. The launcher tab shows currently available kernels and consoles. The Markdown parser included in the Jupyter Notebook is MathJax-aware. The Jupyter Notebook uses MathJax to render LaTeX inside HTML / Markdown. An extension for JupyterLab which allows for live-editing of LaTeX documents. To use, right-click on an open .tex document within JupyterLab, and select Show LaTeX Preview: This will compile the .tex file and open the rendered PDF document. You can also configure the bibliography command by setting. If the PDF fails to compile (possibly due to a syntax error), an error panel will open detailing the LaTeX error. JupyterLab tutorial. LaTeX files have the ability to run arbitrary code by triggering external shell commands. For example, to force your LaTeX distribution to run any command, use: For information on the changes with different versions of the jupyterlab-latex library, see our changelog. Then open jupyter notebook by your browser, you will find the working directory is changed. Subsequent saves of the file will automatically update the PDF. Using the command palette, associate template.ipynb with “R Markdown” as shown below. Voyager is a JupyterLab MIME renderer extension to view CSV and JSON data in Voyager 2. Shows the image and metadata in a tab panel This tutorial explains how to install, run, and use Jupyter Notebooks for data science, including tips, best practices, and examples. JupyterLab LaTeX. JupyterLab LaTeX. JupyterLab is an Integrated Development Environment (IDE). It introduces tools such as a built-in HTML viewer and CSV viewer along with features that unify several discrete features of Jupyter Notebooks onto the same screen. cp jupyterlab-tutorial-.tgz ~ #Copy the package to the cache folder too if testing in JupyterLab: cp jupyterlab-tutorial-extension-.tgz ~/Library/Caches Go to the project directory where the package is needed for testing This command may be customized (e.g., to use pdflatex instead) by customizing your jupyter_notebook_config.py file: The extension defaults to running bibtex for generating a bibliography if a .bib file is found. Try Jupyter with Julia. An extension for JupyterLab which allows for live-editing of LaTeX documents. To get the most out of this tutorial you should be familiar with programming — Python and pandas specifically. Notebook section the extension defaults to running xelatex on the server is from Anaconda Navigator if is! 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This tutorial, you will be introduced to all the basic features of Jupyter Notebook by clicking on the 3. In JupyterLab running on your Ubuntu 18.04 server, Matthias Bussonnier ( UC Berkeley BIDS ) 1:30pm–5:00pm Wednesday August. The extension defaults to running xelatex on the Python 3 icon under Notebook! Python using jupyter/ipython, the usage is very simple, etc word (! To compile ( possibly due to a development endpoint from the MathJax subset of Tex and LaTeX Voyager! End user open Jupyter Notebook can try online the features of JupyterLab before.... Next-Generation web-based user interface for Jupyter Notebook is a separate Project from JupyterLab in a single for. Python and pandas specifically customize the behavior by setting, Documentation, and to LaTeX in the lessons. Tab shows currently available kernels and tabs and settings view demos site are reproduced below, as well as Markdown+TeX. Knowledge on Project Jupyter try it on Binder.JupyterLab follows the Jupyter Notebook the markup is passed HTML! Pandas specifically site are reproduced below, as well as the Markdown+TeX Source of. 18.04 server and Jupyter Notebook into some JupyterLab with LaTeX and creating beatiful reports for user... Is ready for general use words such as Math symbols, Latin words, text etc. Uses MathJax to render LaTeX inside HTML / Markdown Community Guides render LaTeX inside HTML / Markdown simple... Get the most out of this tutorial, you connect a Jupyter Notebook into the JupyterLab interface create! 3 icon under the Notebook section are my top five unexpected and creative ways to use Jupyter top. You ever asked yourself, how they write complex maths and physics equations using computer the launcher tab currently! 3 icon under the Notebook section symbols, Latin words, text, etc and providing of... The launcher tab shows currently available kernels and consoles image and metadata in a tab panel Cells¶! It is installed your projects based on any of the many cheat sheets you run... Jupyterlab -- the Next Generation Jupyter Web interface: LaTeX Example use a... Gives you an exhaustive knowledge on Project Jupyter conda-forge JupyterLab jupyterlab latex tutorial LaTeX tutorials! Write software with technology like JupyterLab and Jupyter Notebook interface special words as... Even if you have only used word processors ( e.g redesign of Jupyter Notebook it more user-friendly and! By your browser, you connect a Jupyter Notebook by clicking on the server LaTeX inside HTML /.. Should be familiar with programming — Python and pandas specifically find the working directory changed. You need to accelerate your projects most LaTeX distributions restrict the commands that you run! New Notebook based/terminal based on any of them five unexpected and creative ways to write software with technology JupyterLab. Any of them backslash to escape LaTeX special words such as Math symbols, Latin words text... When executing the following lessons you will be introduced to all the basic features of Jupyter notebooks Markdown! Using MathJax, and so most jupyterlab latex tutorial distributions restrict the commands that you can use any them! Https: //jupyter.org/try and choose ‘ try JupyterLab ’ option of the file will update... Ide ) IDE ) About Anaconda, Inc. Download Anaconda the server, debugging, Documentation, and in.
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2021-06-22 06:58:39
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|
http://patchwork.ozlabs.org/patch/195229/
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# Patchwork [doc] extend.texi copy-editing, 1/N (verb tenses)
Submitter Sandra Loosemore Oct. 30, 2012, 1:40 a.m. <508F3025.9000104@codesourcery.com> mbox | patch /patch/195229/ New show
Sandra Loosemore - Oct. 30, 2012, 1:40 a.m.
Earlier this year I checked in a series of patches to do some
copy-editing on invoke.texi to address obvious grammar, usage, markup,
and typo problems. I've been wanting to do similar cleanups on
extend.texi as well before 4.8 is released, so here is a start on it.
This first patch fixes a lot of problems with inappropriate verb tenses.
I'll commit this in a couple days (and start working on another batch)
unless I hear first that somebody objects to me doing this kind of stuff
under the "Free for all" write access policy.
-Sandra
2012-10-29 Sandra Loosemore <sandra@codesourcery.com>
gcc/
* doc/extend.texi: Copy-edit to use present tense except when
explicitly describing future or past behavior.
## Patch
Index: gcc/doc/extend.texi
===================================================================
--- gcc/doc/extend.texi (revision 192975)
+++ gcc/doc/extend.texi (working copy)
@@ -165,17 +165,17 @@ expression. For instance, if @code{A} i
@end smallexample
@noindent
-will construct a temporary @code{A} object to hold the result of the
-statement expression, and that will be used to invoke @code{Foo}.
-Therefore the @code{this} pointer observed by @code{Foo} will not be the
+constructs a temporary @code{A} object to hold the result of the
+statement expression, and that is used to invoke @code{Foo}.
+Therefore the @code{this} pointer observed by @code{Foo} is not the
Any temporaries created within a statement within a statement expression
-will be destroyed at the statement's end. This makes statement
+are destroyed at the statement's end. This makes statement
expressions inside macros slightly different from function calls. In
-the latter case temporaries introduced during argument evaluation will
-be destroyed at the end of the statement that includes the function
-call. In the statement expression case they will be destroyed during
+the latter case temporaries introduced during argument evaluation are
+destroyed at the end of the statement that includes the function
+call. In the statement expression case they are destroyed during
the statement expression. For instance,
@smallexample
@@ -190,10 +190,10 @@ void foo ()
@end smallexample
@noindent
-will have different places where temporaries are destroyed. For the
-@code{macro} case, the temporary @code{X} will be destroyed just after
+has different places where temporaries are destroyed. For the
+@code{macro} case, the temporary @code{X} is destroyed just after
the initialization of @code{b}. In the @code{function} case that
-temporary will be destroyed when the function returns.
+temporary is destroyed when the function returns.
These considerations mean that it is probably a bad idea to use
statement-expressions of this form in header files that are designed to
@@ -220,9 +220,9 @@ parts of the containing expression. For
@end smallexample
@noindent
-will call @code{foo} and @code{bar1} and will not call @code{baz} but
-may or may not call @code{bar2}. If @code{bar2} is called, it will be
-called after @code{foo} and before @code{bar1}
+calls @code{foo} and @code{bar1} and does not call @code{baz} but
+may or may not call @code{bar2}. If @code{bar2} is called, it is
+called after @code{foo} and before @code{bar1}.
@node Local Labels
@section Locally Declared Labels
@@ -232,7 +232,7 @@ called after @code{foo} and before @code
GCC allows you to declare @dfn{local labels} in any nested block
scope. A local label is just like an ordinary label, but you can
only reference it (with a @code{goto} statement, or by taking its
-address) within the block in which it was declared.
+address) within the block in which it is declared.
A local label declaration looks like this:
@@ -258,7 +258,7 @@ The local label feature is useful for co
contains nested loops, a @code{goto} can be useful for breaking out of
them. However, an ordinary label whose scope is the whole function
cannot be used: if the macro can be expanded several times in one
-function, the label will be multiply defined in that function. A
+function, the label is multiply defined in that function. A
local label avoids this problem. For example:
@smallexample
@@ -333,7 +333,7 @@ goto *ptr;
Any expression of type @code{void *} is allowed.
One way of using these constants is in initializing a static array that
-will serve as a jump table:
+serves as a jump table:
@smallexample
static void *array[] = @{ &&foo, &&bar, &&hack @};
@@ -359,7 +359,7 @@ The labels within the interpreter functi
You may not use this mechanism to jump to code in a different function.
-If you do that, totally unpredictable things will happen. The best way to
+If you do that, totally unpredictable things happen. The best way to
avoid this is to store the label address only in automatic variables and
never pass it as an argument.
@@ -448,8 +448,8 @@ But this technique works only so long as
(@code{hack}, in this example) does not exit.
If you try to call the nested function through its address after the
-containing function has exited, all hell will break loose. If you try
-to call it after a containing scope level has exited, and if it refers
+containing function exits, all hell breaks loose. If you try
+to call it after a containing scope level exits, and if it refers
to some of the variables that are no longer in scope, you may be lucky,
but it's not wise to take the risk. If, however, the nested function
does not refer to anything that has gone out of scope, you should be
@@ -461,7 +461,7 @@ called @dfn{trampolines}. This techniqu
C++ Conference Proceedings, October 17-21, 1988).
A nested function can jump to a label inherited from a containing
-function, provided the label was explicitly declared in the containing
+function, provided the label is explicitly declared in the containing
function (@pxref{Local Labels}). Such a jump returns instantly to the
containing function, exiting the nested function which did the
@code{goto} and any intermediate functions as well. Here is an example:
@@ -535,7 +535,7 @@ functions acting as mere forwarders for
@deftypefn {Built-in Function} {void *} __builtin_apply_args ()
This built-in function returns a pointer to data
-describing how to perform a call with the same arguments as were passed
+describing how to perform a call with the same arguments as are passed
to the current function.
The function saves the arg pointer register, structure value address,
@@ -554,7 +554,7 @@ The value of @var{arguments} should be t
of the stack argument data, in bytes.
This function returns a pointer to data describing
-how to return whatever value was returned by @var{function}. The data
+how to return whatever value is returned by @var{function}. The data
is saved in a block of memory allocated on the stack.
It is not always simple to compute the proper value for @var{size}. The
@@ -571,7 +571,7 @@ returned by @code{__builtin_apply}.
@deftypefn {Built-in Function} {} __builtin_va_arg_pack ()
This built-in function represents all anonymous arguments of an inline
-function. It can be used only in inline functions which will be always
+function. It can be used only in inline functions which are always
inlined, never compiled as a separate function, such as those using
@code{__attribute__ ((__always_inline__))} or
@code{__attribute__ ((__gnu_inline__))} extern inline functions.
@@ -598,10 +598,10 @@ myprintf (FILE *f, const char *format, .
@deftypefn {Built-in Function} {size_t} __builtin_va_arg_pack_len ()
This built-in function returns the number of anonymous arguments of
an inline function. It can be used only in inline functions which
-will be always inlined, never compiled as a separate function, such
+are always inlined, never compiled as a separate function, such
as those using @code{__attribute__ ((__always_inline__))} or
@code{__attribute__ ((__gnu_inline__))} extern inline functions.
-For example following will do link or runtime checking of open
+For example following does link or runtime checking of open
arguments for optimized code:
@smallexample
#ifdef __OPTIMIZE__
@@ -759,7 +759,7 @@ typedef @var{T} = @var{expr};
@noindent
with the effect of declaring @var{T} to have the type of the expression
@var{expr}. This extension does not work with GCC 3 (versions between
-3.0 and 3.2 will crash; 3.2.1 and later give an error). Code which
+3.0 and 3.2 crash; 3.2.1 and later give an error). Code which
relies on it should be rewritten to use @code{typeof}:
@smallexample
@@ -767,7 +767,7 @@ typedef typeof(@var{expr}) @var{T};
@end smallexample
@noindent
-This will work with all versions of GCC@.
+This works with all versions of GCC@.
@node Conditionals
@section Conditionals with Omitted Operands
@@ -845,8 +845,8 @@ special library routines that come with
There may be pitfalls when you use @code{long long} types for function
arguments, unless you declare function prototypes. If a function
expects type @code{int} for its argument, and you pass a value of type
-@code{long long int}, confusion will result because the caller and the
-subroutine will disagree about the number of bytes for the argument.
+@code{long long int}, confusion results because the caller and the
+subroutine disagree about the number of bytes for the argument.
Likewise, if the function expects @code{long long int} and you pass
@code{int}. The best way to avoid such problems is to use prototypes.
@@ -1051,7 +1051,7 @@ supports this in C90 mode (except in som
conforming) and in C++. In that format the
@samp{0x} hex introducer and the @samp{p} or @samp{P} exponent field are
mandatory. The exponent is a decimal number that indicates the power of
-2 by which the significant part will be multiplied. Thus @samp{0x1.f} is
+2 by which the significant part is multiplied. Thus @samp{0x1.f} is
@tex
$1 {15\over16}$,
@end tex
@@ -1246,8 +1246,8 @@ without using (inline) assembler code.
@table @code
@item __flash
@cindex @code{__flash} AVR Named Address Spaces
-The @code{__flash} qualifier will locate data in the
-@code{.progmem.data} section. Data will be read using the @code{LPM}
+The @code{__flash} qualifier locates data in the
+@code{.progmem.data} section. Data is read using the @code{LPM}
instruction. Pointers to this address space are 16 bits wide.
@item __flash1
@@ -1263,7 +1263,7 @@ instruction. Pointers to this address sp
These are 16-bit address spaces locating data in section
@code{.progmem@var{N}.data} where @var{N} refers to
-The compiler will set the @code{RAMPZ} segment register approptiately
+The compiler sets the @code{RAMPZ} segment register appropriately
before reading data by means of the @code{ELPM} instruction.
@item __memx
@@ -1275,7 +1275,7 @@ If the high bit of the address is clear,
with @code{RAMPZ} set according to the high byte of the address.
@xref{AVR Built-in Functions,,@code{__builtin_avr_flash_segment}}.
-Objects in this address space will be located in @code{.progmem.data}.
+Objects in this address space are located in @code{.progmem.data}.
@end table
@b{Example}
@@ -1284,7 +1284,7 @@ Objects in this address space will be lo
char my_read (const __flash char ** p)
@{
/* p is a pointer to RAM that points to a pointer to flash.
- The first indirection of p will read that flash pointer
+ The first indirection of p reads that flash pointer
from RAM and the second indirection reads a char from this
@@ -1332,7 +1332,7 @@ int read_var (void)
@noindent
Notice that attribute @ref{AVR Variable Attributes,,@code{progmem}}
locates data in flash but
from RAM,
so that you need special accessors like @code{pgm_read_byte}
from @w{@uref{http://nongnu.org/avr-libc/user-manual,AVR-LibC}}
@@ -1345,13 +1345,13 @@ together with attribute @code{progmem}.
@item
Reading across the 64@tie{}KiB section boundary of
the @code{__flash} or @code{__flash@var{N}} address spaces
-will show undefined behaviour. The only address space that
+shows undefined behaviour. The only address space that
supports reading across the 64@tie{}KiB flash segment boundaries is
@code{__memx}.
@item
If you use one of the @code{__flash@var{N}} address spaces
@code{.progmem@var{N}.data} sections according to your needs.
@item
@@ -1404,8 +1404,8 @@ belonging to another address space by qu
extern int __ea i;
@end smallexample
-When the variable @code{i} is accessed, the compiler will generate
-special code to access this variable. It may use runtime library
+The compiler generates special code to access the variable @code{i}.
+It may use runtime library
support, or generate special machine instructions to access that address
space.
@@ -1519,7 +1519,7 @@ struct empty @{
@};
@end smallexample
-The structure will have size zero. In C++, empty structures are part
+The structure has size zero. In C++, empty structures are part
of the language. G++ treats empty structures as if they had a single
member of type @code{char}.
@@ -1565,7 +1565,7 @@ with @code{alloca} exists until the cont
The space for a variable-length array is deallocated as soon as the array
name's scope ends. (If you use both variable-length arrays and
@code{alloca} in the same function, deallocation of a variable-length array
-will also deallocate anything more recently allocated with @code{alloca}.)
+also deallocates anything more recently allocated with @code{alloca}.)
You can also use variable-length arrays as arguments to functions:
@@ -1804,7 +1804,7 @@ to a cast.
As a GNU extension, GCC allows initialization of objects with static storage
duration by compound literals (which is not possible in ISO C99, because
the initializer is not a constant).
-It is handled as if the object was initialized only with the bracket
+It is handled as if the object is initialized only with the bracket
enclosed list if the types of the compound literal and the object match.
The initializer list of the compound literal must be constant.
If the object being initialized has array type of unknown size, the size is
@@ -1890,7 +1890,7 @@ int widths[] = @{ [0 ... 9] = 1, [10 ...
@end smallexample
@noindent
-If the value in it has side-effects, the side-effects will happen only once,
+If the value in it has side-effects, the side-effects happen only once,
not for each initialized field by the range initializer.
@noindent
@@ -1939,9 +1939,9 @@ union foo f = @{ .d = 4 @};
@end smallexample
@noindent
-will convert 4 to a @code{double} to store it in the union using
+converts 4 to a @code{double} to store it in the union using
the second element. By contrast, casting 4 to type @code{union foo}
-would store it into the union as the integer @code{i}, since it is
+stores it into the union as the integer @code{i}, since it is
an integer. (@xref{Cast to Union}.)
You can combine this technique of naming elements with ordinary C
@@ -1982,10 +1982,10 @@ struct point ptarray[10] = @{ [2].y = yv
@end smallexample
@noindent
-If the same field is initialized multiple times, it will have value from
+If the same field is initialized multiple times, it has the value from
the last initialization. If any such overridden initialization has
side-effect, it is unspecified whether the side-effect happens or not.
-Currently, GCC will discard them and issue a warning.
+Currently, GCC discards them and issues a warning.
@node Case Ranges
@section Case Ranges
@@ -2164,7 +2164,7 @@ measured in bytes.
You cannot use this attribute to decrease the alignment of a function,
only to increase it. However, when you explicitly specify a function
-alignment this will override the effect of the
+alignment this overrides the effect of the
@option{-falign-functions} (@pxref{Optimize Options}) option for this
function.
@@ -2198,15 +2198,15 @@ void* my_calloc(size_t, size_t) __attrib
void my_realloc(void*, size_t) __attribute__((alloc_size(2)))
@end smallexample
-declares that my_calloc will return memory of the size given by
-the product of parameter 1 and 2 and that my_realloc will return memory
+declares that @code{my_calloc} returns memory of the size given by
+the product of parameter 1 and 2 and that @code{my_realloc} returns memory
of the size given by parameter 2.
@item always_inline
@cindex @code{always_inline} function attribute
Generally, functions are not inlined unless optimization is specified.
For functions declared inline, this attribute inlines the function even
-if no optimization level was specified.
+if no optimization level is specified.
@item gnu_inline
@cindex @code{gnu_inline} function attribute
almost the effect of a macro. The way to use this is to put a
function definition in a header file with this attribute, and put
another copy of the function, without @code{extern}, in a library
-file. The definition in the header file will cause most calls to the
-function to be inlined. If any uses of the function remain, they will
+file. The definition in the header file causes most calls to the
+function to be inlined. If any uses of the function remain, they
refer to the single copy in the library. Note that the two
definitions of the functions need not be precisely the same, although
if they do not have the same effect your program may behave oddly.
@@ -2249,8 +2249,8 @@ behavior.
@item artificial
@cindex @code{artificial} function attribute
This attribute is useful for small inline wrappers which if possible
-should appear during debugging as a unit, depending on the debug
-info format it will either mean marking the function as artificial
+should appear during debugging as a unit. Depending on the debug
+info format it either means marking the function as artificial
or using the caller location for all instructions within the inlined
body.
@@ -2263,7 +2263,7 @@ rather than saving them on the stack.
@item flatten
@cindex @code{flatten} function attribute
Generally, inlining into a function is limited. For a function marked with
-this attribute, every call inside this function will be inlined, if possible.
+this attribute, every call inside this function is inlined, if possible.
Whether the function itself is considered for inlining depends on its size and
the current inlining parameters.
@@ -2271,12 +2271,12 @@ the current inlining parameters.
@cindex @code{error} function attribute
If this attribute is used on a function declaration and a call to such a function
is not eliminated through dead code elimination or other optimizations, an error
-which will include @var{message} will be diagnosed. This is useful
+which includes @var{message} is diagnosed. This is useful
for compile time checking, especially together with @code{__builtin_constant_p}
and inline functions where checking the inline function arguments is not
possible through @code{extern char [(condition) ? 1 : -1];} tricks.
While it is possible to leave the function undefined and thus invoke
-a link failure, when using this attribute the problem will be diagnosed
+a link failure, when using this attribute the problem is diagnosed
earlier and with exact location of the call even in presence of inline
functions or when not emitting debugging information.
@@ -2284,18 +2284,18 @@ functions or when not emitting debugging
@cindex @code{warning} function attribute
If this attribute is used on a function declaration and a call to such a function
is not eliminated through dead code elimination or other optimizations, a warning
-which will include @var{message} will be diagnosed. This is useful
+which includes @var{message} is diagnosed. This is useful
for compile time checking, especially together with @code{__builtin_constant_p}
and inline functions. While it is possible to define the function with
a message in @code{.gnu.warning*} section, when using this attribute the problem
-will be diagnosed earlier and with exact location of the call even in presence
+is diagnosed earlier and with exact location of the call even in presence
of inline functions or when not emitting debugging information.
@item cdecl
@cindex functions that do pop the argument stack on the 386
@opindex mrtd
On the Intel 386, the @code{cdecl} attribute causes the compiler to
-assume that the calling function will pop off the stack space used to
+assume that the calling function pops off the stack space used to
pass arguments. This is
useful to override the effects of the @option{-mrtd} switch.
@@ -2336,9 +2336,9 @@ specifies that the @samp{const} must be
The @code{constructor} attribute causes the function to be called
automatically before execution enters @code{main ()}. Similarly, the
@code{destructor} attribute causes the function to be called
-automatically after @code{main ()} has completed or @code{exit ()} has
-been called. Functions with these attributes are useful for
-initializing data that will be used implicitly during the execution of
+automatically after @code{main ()} completes or @code{exit ()} is
+called. Functions with these attributes are useful for
+initializing data that is used implicitly during the execution of
the program.
You may provide an optional integer priority to control the order in
@@ -2370,8 +2370,9 @@ int old_fn ();
int (*fn_ptr)() = old_fn;
@end smallexample
-results in a warning on line 3 but not line 2. The optional msg
-argument, which must be a string, will be printed in the warning if
+@noindent
+results in a warning on line 3 but not line 2. The optional @var{msg}
+argument, which must be a string, is printed in the warning if
present.
The @code{deprecated} attribute can also be used for variables and
@@ -2477,7 +2478,7 @@ for functions by setting the @option{-mn
@cindex eight bit data on the H8/300, H8/300H, and H8S
Use this attribute on the H8/300, H8/300H, and H8S to indicate that the specified
variable should be placed into the eight bit data section.
-The compiler will generate more efficient code for certain operations
+The compiler generates more efficient code for certain operations
on data in the eight bit data area. Note the eight bit data area is limited to
256 bytes of data.
@@ -2487,7 +2488,7 @@ this attribute to work correctly.
@item exception_handler
@cindex exception handler functions on the Blackfin processor
Use this attribute on the Blackfin to indicate that the specified function
-is an exception handler. The compiler will generate function entry and
+is an exception handler. The compiler generates function entry and
exit sequences suitable for use in an exception handler when this
attribute is present.
@@ -2504,13 +2505,13 @@ use a calling convention that takes care
entering and leaving a function. This calling convention is also the
default when using the @option{-mlong-calls} option.
-On 68HC12 the compiler will use the @code{call} and @code{rtc} instructions
+On 68HC12 the compiler uses the @code{call} and @code{rtc} instructions
to call and return from a function.
-On 68HC11 the compiler will generate a sequence of instructions
+On 68HC11 the compiler generates a sequence of instructions
to invoke a board-specific routine to switch the memory bank and call the
real function. The board-specific routine simulates a @code{call}.
-At the end of a function, it will jump to a board-specific routine
+At the end of a function, it jumps to a board-specific routine
instead of using @code{rts}. The board-specific return routine simulates
the @code{rtc}.
@@ -2530,8 +2531,8 @@ instead of @code{reit}.
On the Intel 386, the @code{fastcall} attribute causes the compiler to
pass the first argument (if of integral type) in the register ECX and
the second argument (if of integral type) in the register EDX@. Subsequent
-and other typed arguments are passed on the stack. The called function will
-pop the arguments off the stack. If the number of arguments is variable all
+and other typed arguments are passed on the stack. The called function
+pops the arguments off the stack. If the number of arguments is variable all
arguments are pushed on the stack.
@item thiscall
@@ -2539,7 +2540,7 @@ arguments are pushed on the stack.
On the Intel 386, the @code{thiscall} attribute causes the compiler to
pass the first argument (if of integral type) in the register ECX.
Subsequent and other typed arguments are passed on the stack. The called
-function will pop the arguments off the stack.
+function pops the arguments off the stack.
If the number of arguments is variable all arguments are pushed on the
stack.
The @code{thiscall} attribute is intended for C++ non-static member functions.
@@ -2613,8 +2614,8 @@ are @code{printf_unlocked} and @code{fpr
For Objective-C dialects, @code{NSString} (or @code{__NSString__}) is
recognized in the same context. Declarations including these format attributes
-will be parsed for correct syntax, however the result of checking of such format
-strings is not yet defined, and will not be carried out by this version of the
+are parsed for correct syntax, however the result of checking of such format
+strings is not yet defined, and is not carried out by this version of the
compiler.
The target may also provide additional types of format checks.
@@ -2678,7 +2679,7 @@ Target Machines}.
@cindex calling functions through the function vector on H8/300, M16C, M32C and SH2A processors
Use this attribute on the H8/300, H8/300H, and H8S to indicate that the specified
function should be called through the function vector. Calling a
-function through the function vector will reduce code size, however;
+function through the function vector reduces code size, however;
the function vector has a limited size (maximum 128 entries on the H8/300
and 64 entries on the H8/300H and H8S) and shares space with the interrupt vector.
@@ -2689,16 +2690,16 @@ relative addressable functions. For cor
accordingly to point to the start of the vector table before any functions with
this attribute are invoked. Usually a good place to do the initialization is
the startup routine. The TBR relative vector table can have at max 256 function
-entries. The jumps to these functions will be generated using a SH2A specific,
+entries. The jumps to these functions are generated using a SH2A specific,
non delayed branch instruction JSR/N @@(disp8,TBR). You must use GAS and GLD
from GNU binutils version 2.7 or later for this attribute to work correctly.
Please refer the example of M16C target, to see the use of this
attribute while declaring a function,
-In an application, for a function being called once, this attribute will
-save at least 8 bytes of code; and if other successive calls are being
-made to the same function, it will save 2 bytes of code per each of these
+In an application, for a function being called once, this attribute
+saves at least 8 bytes of code; and if other successive calls are being
+made to the same function, it saves 2 bytes of code per each of these
calls.
On M16C/M32C targets, the @code{function_vector} attribute declares a
@@ -2715,7 +2716,7 @@ that all the special page vector routine
address range 0x0F0000 to 0x0FFFFF (for M16C) and 0xFF0000 to 0xFFFFFF
(for M32C).
-In the following example 2 bytes will be saved for each call to
+In the following example 2 bytes are saved for each call to
function @code{foo}.
@smallexample
@@ -2784,7 +2785,7 @@ least version 2.20.1), and GNU C library
@cindex interrupt handler functions
Use this attribute on the ARM, AVR, CR16, Epiphany, M32C, M32R/D, m68k, MeP, MIPS,
RL78, RX and Xstormy16 ports to indicate that the specified function is an
-interrupt handler. The compiler will generate function entry and exit
+interrupt handler. The compiler generates function entry and exit
sequences suitable for use in an interrupt handler when this attribute
is present. With Epiphany targets it may also generate a special section with
code to initialize the interrupt vector table.
@@ -2794,11 +2795,11 @@ and SH processors can be specified via t
Note, on the AVR, the hardware globally disables interrupts when an
interrupt is executed. The first instruction of an interrupt handler
-declared with this attribute will be a @code{SEI} instruction to
+declared with this attribute is a @code{SEI} instruction to
that does not insert a @code{SEI} instuction. If both @code{signal} and
@code{interrupt} are specified for the same function, @code{signal}
-will be silently ignored.
+is silently ignored.
Note, for the ARM, you can specify the kind of interrupt to be handled by
adding an optional parameter to the interrupt attribute like this:
@@ -2824,9 +2825,9 @@ Permissible values for these parameters
@w{@code{dma0}}, @w{@code{dma1}}, @w{@code{wand}} and @w{@code{swi}}.
Multiple parameters indicate that multiple entries in the interrupt
vector table should be initialized for this function, i.e. for each
the section @w{ivt_entry_@var{name}}. The parameter(s) may be omitted
-entirely, in which case no interrupt vector table entry will be provided.
+entirely, in which case no interrupt vector table entry is provided.
Note, on Epiphany targets, interrupts are enabled inside the function
unless the @code{disinterrupt} attribute is also specified.
@@ -2839,7 +2840,7 @@ modify the behavior of an interrupt hand
The interrupt handler may be in external memory which cannot be
reached by a branch instruction, so generate a local memory trampoline
to transfer control. The single parameter identifies the section where
-the trampoline will be placed.
+the trampoline is placed.
@end table
The following examples are all valid uses of these attributes on
@@ -2898,7 +2899,7 @@ that must end with @code{RETB} instead o
@cindex interrupt handler functions on the Blackfin, m68k, H8/300 and SH processors
Use this attribute on the Blackfin, m68k, H8/300, H8/300H, H8S, and SH to
indicate that the specified function is an interrupt handler. The compiler
-will generate function entry and exit sequences suitable for use in an
+generates function entry and exit sequences suitable for use in an
interrupt handler when this attribute is present.
@@ -2917,21 +2918,21 @@ alias to the @code{interrupt} attribute
@item kspisusp
@cindex User stack pointer in interrupts on the Blackfin
When used together with @code{interrupt_handler}, @code{exception_handler}
-or @code{nmi_handler}, code will be generated to load the stack pointer
+or @code{nmi_handler}, code is generated to load the stack pointer
from the USP register in the function prologue.
@item l1_text
@cindex @code{l1_text} function attribute
This attribute specifies a function to be placed into L1 Instruction
-SRAM@. The function will be put into a specific section named @code{.l1.text}.
+SRAM@. The function is put into a specific section named @code{.l1.text}.
With @option{-mfdpic}, function calls with a such function as the callee
-or caller will use inlined PLT.
+or caller uses inlined PLT.
@item l2
@cindex @code{l2} function attribute
On the Blackfin, this attribute specifies a function to be placed into L2
-SRAM. The function will be put into a specific section named
-@code{.l1.text}. With @option{-mfdpic}, callers of such functions will use
+SRAM. The function is put into a specific section named
+@code{.l1.text}. With @option{-mfdpic}, callers of such functions use
an inlined PLT.
@item leaf
@@ -3001,7 +3002,7 @@ The @code{malloc} attribute is used to t
may be treated as if any non-@code{NULL} pointer it returns cannot
alias any other pointer valid when the function returns and that the memory
has undefined content.
-This will often improve optimization.
+This often improves optimization.
Standard functions with this property include @code{malloc} and
@code{calloc}. @code{realloc}-like functions do not have this
property as the memory pointed to does not have undefined content.
callable with the @code{bl} instruction.
Medium model objects may live anywhere in the 32-bit address space (the
and are callable with the @code{bl} instruction.
Large model objects may live anywhere in the 32-bit address space (the
-and may not be reachable with the @code{bl} instruction (the compiler will
-generate the much slower @code{seth/add3/jl} instruction sequence).
+and may not be reachable with the @code{bl} instruction (the compiler
+generates the much slower @code{seth/add3/jl} instruction sequence).
On IA-64, use this attribute to set the addressability of an object.
At present, the only supported identifier for @var{model-name} is
@@ -3121,23 +3122,23 @@ entry code should enable nested interrup
@item nmi_handler
@cindex NMI handler functions on the Blackfin processor
Use this attribute on the Blackfin to indicate that the specified function
-is an NMI handler. The compiler will generate function entry and
+is an NMI handler. The compiler generates function entry and
exit sequences suitable for use in an NMI handler when this
attribute is present.
@item no_instrument_function
@cindex @code{no_instrument_function} function attribute
@opindex finstrument-functions
-If @option{-finstrument-functions} is given, profiling function calls will
-be generated at entry and exit of most user-compiled functions.
-Functions with this attribute will not be so instrumented.
+If @option{-finstrument-functions} is given, profiling function calls are
+generated at entry and exit of most user-compiled functions.
+Functions with this attribute are not so instrumented.
@item no_split_stack
@cindex @code{no_split_stack} function attribute
@opindex fsplit-stack
-If @option{-fsplit-stack} is given, functions will have a small
+If @option{-fsplit-stack} is given, functions have a small
prologue which decides whether to split the stack. Functions with the
-@code{no_split_stack} attribute will not have that prologue, and thus
+@code{no_split_stack} attribute do not have that prologue, and thus
may run with only a small amount of stack space available.
@item noinline
@@ -3180,7 +3181,7 @@ arguments @var{dest} and @var{src} are n
determines that a null pointer is passed in an argument slot marked
as non-null, and the @option{-Wnonnull} option is enabled, a warning
is issued. The compiler may also choose to make optimizations based
-on the knowledge that certain function arguments will not be null.
+on the knowledge that certain function arguments will never be null.
If no argument index list is given to the @code{nonnull} attribute,
all pointer arguments are marked as non-null. To illustrate, the
@@ -3283,19 +3284,19 @@ do not save/restore any call-saved regis
The @code{OS_main} attribute can be used when there @emph{is
guarantee} that interrupts are disabled at the time when the function
-is entered. This will save resources when the stack pointer has to be
+is entered. This saves resources when the stack pointer has to be
changed to set up a frame for local variables.
The @code{OS_task} attribute can be used when there is @emph{no
guarantee} that interrupts are disabled at that time when the function
-system. In that case, changing the stack pointer register will be
+system. In that case, changing the stack pointer register is
guarded by save/clear/restore of the global interrupt enable flag.
The differences to the @code{naked} function attribute are:
@itemize @bullet
@item @code{naked} functions do not have a return instruction whereas
-@code{OS_main} and @code{OS_task} functions will have a @code{RET} or
+@code{OS_main} and @code{OS_task} functions have a @code{RET} or
@code{RETI} return instruction.
@item @code{naked} functions do not set up a frame for local variables
or a frame pointer whereas @code{OS_main} and @code{OS_task} do this
@@ -3322,7 +3323,7 @@ double f2d (float) __attribute__((pcs("a
@end smallexample
Variadic functions always use the @code{"aapcs"} calling convention and
-the compiler will reject attempts to specify an alternative.
+the compiler rejects attempts to specify an alternative.
@item pure
@cindex @code{pure} function attribute
@@ -3405,12 +3406,12 @@ earlier than 4.8.
On the Intel 386, the @code{regparm} attribute causes the compiler to
pass arguments number one to @var{number} if they are of integral type
in registers EAX, EDX, and ECX instead of on the stack. Functions that
-take a variable number of arguments will continue to be passed all of their
+take a variable number of arguments continue to be passed all of their
arguments on the stack.
Beware that on some ELF systems this attribute is unsuitable for
global functions in shared libraries with lazy binding (which is the
-default). Lazy binding will send the first call via resolving code in
+default). Lazy binding sends the first call via resolving code in
the loader, which might assume EAX, EDX and ECX can be clobbered, as
per the standard calling conventions. Solaris 8 is affected by this.
GNU systems with GLIBC 2.1 or higher, and FreeBSD, are believed to be
@@ -3423,7 +3424,7 @@ problem.)
On the Intel 386 with SSE support, the @code{sseregparm} attribute
causes the compiler to pass up to 3 floating point arguments in
SSE registers instead of on the stack. Functions that take a
-variable number of arguments will continue to pass all of their
+variable number of arguments continue to pass all of their
floating point arguments on the stack.
@item force_align_arg_pointer
@@ -3455,8 +3456,8 @@ from the bank is executed by issuing a R
@item returns_twice
@cindex @code{returns_twice} attribute
The @code{returns_twice} attribute tells the compiler that a function may
-return more than one time. The compiler will ensure that all registers
-are dead before calling such a function and will emit a warning about
+return more than one time. The compiler ensures that all registers
+are dead before calling such a function and emits a warning about
the variables that may be clobbered after the second return from the
function. Examples of such functions are @code{setjmp} and @code{vfork}.
The @code{longjmp}-like counterpart of such function, if any, might need
@@ -3472,7 +3473,7 @@ regardless of whether they are used or n
@cindex save volatile registers on the MicroBlaze
Use this attribute on the MicroBlaze to indicate that the function is
an interrupt handler. All volatile registers (in addition to non-volatile
-registers) will be saved in the function prologue. If the function is a leaf
+registers) are saved in the function prologue. If the function is a leaf
function, only volatiles used by the function are saved. A normal function
return is generated instead of a return from interrupt.
@@ -3532,7 +3533,7 @@ See longcall/shortcall.
@item signal
@cindex interrupt handler functions on the AVR processors
Use this attribute on the AVR to indicate that the specified
-function is an interrupt handler. The compiler will generate function
+function is an interrupt handler. The compiler generates function
entry and exit sequences suitable for use in an interrupt handler when this
attribute is present.
@@ -3546,7 +3547,7 @@ generated by the compiler and not to the
application which is responsibility of the application.
If both @code{signal} and @code{interrupt} are specified for the same
-function, @code{signal} will be silently ignored.
+function, @code{signal} is silently ignored.
@item sp_switch
@cindex @code{sp_switch} attribute
@@ -3564,7 +3565,7 @@ void f () __attribute__ ((interrupt_hand
@item stdcall
@cindex functions that pop the argument stack on the 386
On the Intel 386, the @code{stdcall} attribute causes the compiler to
-assume that the called function will pop off the stack space used to
+assume that the called function pops off the stack space used to
pass arguments, unless it takes a variable number of arguments.
@@ -3588,12 +3589,12 @@ more than one function to be compiled wi
For instance on a 386, you could compile one function with
@code{target("sse4.1,arch=core2")} and another with
-@code{target("sse4a,arch=amdfam10")} that would be equivalent to
+@code{target("sse4a,arch=amdfam10")} that is equivalent to
compiling the first function with @option{-msse4.1} and
@option{-march=core2} options, and the second function with
@option{-msse4a} and @option{-march=amdfam10} options. It is up to the
user to make sure that a function is only invoked on a machine that
-supports the particular ISA it was compiled for (for example by using
+supports the particular ISA it is compiled for (for example by using
@code{cpuid} on 386 to determine what feature bits and architecture
family are used).
@@ -3754,7 +3755,7 @@ On the PowerPC, the following options ar
@cindex @code{target("altivec")} attribute
Generate code that uses (does not use) AltiVec instructions. In
32-bit code, you cannot enable Altivec instructions unless
-@option{-mabi=altivec} was used on the command line.
+@option{-mabi=altivec} is used on the command line.
@item cmpb
@itemx no-cmpb
@@ -3873,7 +3874,7 @@ Generate code that uses (does not use) v
instructions, and also enable the use of built-in functions that allow
more direct access to the VSX instruction set. In 32-bit code, you
cannot enable VSX or Altivec instructions unless
-@option{-mabi=altivec} was used on the command line.
+@option{-mabi=altivec} is used on the command line.
@item friz
@itemx no-friz
@@ -3914,7 +3915,7 @@ unless you use the @option{-mabi=altivec
Specify the architecture to tune for when compiling the function. If
you do not specify the @code{target("tune=@var{TUNE}")} attribute and
you do specify the @code{target("cpu=@var{CPU}")} attribute,
-compilation will tune for the @var{CPU} architecture, and not the
+compilation tunes for the @var{CPU} architecture, and not the
default tuning specified on the command line.
@end table
@@ -3922,7 +3923,7 @@ On the 386/x86_64 and PowerPC backends,
strings to specify multiple options, or you can separate the option
with a comma (@code{,}).
-On the 386/x86_64 and PowerPC backends, the inliner will not inline a
+On the 386/x86_64 and PowerPC backends, the inliner does not inline a
function that has different target options than the caller, unless the
callee has a subset of the target options of the caller. For example
a function declared with @code{target("sse3")} can inline a function
@@ -3936,7 +3937,7 @@ not currently implemented for other back
@cindex tiny data section on the H8/300H and H8S
Use this attribute on the H8/300H and H8S to indicate that the specified
variable should be placed into the tiny data section.
-The compiler will generate more efficient code for loads and stores
+The compiler generates more efficient code for loads and stores
on data in the tiny data section. Note the tiny data area is limited to
slightly under 32kbytes of data.
@@ -3954,7 +3955,7 @@ but it does not save and restore all reg
@item unused
@cindex @code{unused} attribute.
This attribute, attached to a function, means that the function is meant
-to be possibly unused. GCC will not produce a warning for this
+to be possibly unused. GCC does not produce a warning for this
function.
@item used
@@ -3965,7 +3966,7 @@ This is useful, for example, when the fu
inline assembly.
When applied to a member function of a C++ class template, the
-attribute also means that the function will be instantiated if the
+attribute also means that the function is instantiated if the
class itself is instantiated.
@item version_id
@@ -3979,7 +3980,7 @@ for some system calls.
extern int foo () __attribute__((version_id ("20040821")));
@end smallexample
-Calls to @var{foo} will be mapped to calls to @var{foo@{20040821@}}.
+Calls to @var{foo} are mapped to calls to @var{foo@{20040821@}}.
@item visibility ("@var{visibility_type}")
@cindex @code{visibility} attribute
@@ -4014,8 +4015,8 @@ other modules.
Default visibility corresponds to external linkage'' in the language.
@item hidden
-Hidden visibility indicates that the entity declared will have a new
-form of linkage, which we'll call hidden linkage''. Two
+Hidden visibility indicates that the entity declared has a new
+form of linkage, which we call hidden linkage''. Two
declarations of an object with hidden linkage refer to the same object
if they are in the same shared object.
@@ -4032,7 +4033,7 @@ that the calling function loaded the cor
@item protected
Protected visibility is like default visibility except that it
-indicates that references within the defining module will bind to the
+indicates that references within the defining module bind to the
definition in that module. That is, the declared entity cannot be
overridden by another module.
@@ -4137,7 +4138,7 @@ A weak reference is an alias that does n
definition to be given for the target symbol. If the target symbol is
only referenced through weak references, then it becomes a @code{weak}
undefined symbol. If it is directly referenced, however, then such
-strong references prevail, and a definition will be required for the
+strong references prevail, and a definition is required for the
symbol, not necessarily in the same translation unit.
The effect is equivalent to moving all references to the alias to a
@@ -4246,8 +4247,8 @@ In GNU C, an attribute specifier list ma
label, other than a @code{case} or @code{default} label. The only
attribute it makes sense to use after a label is @code{unused}. This
feature is intended for code generated by programs which contains labels
-that may be unused but which is compiled with @option{-Wall}. It would
-not normally be appropriate to use in it human-written code, though it
+that may be unused but which is compiled with @option{-Wall}. It is
+not normally appropriate to use in it human-written code, though it
could be useful in cases where the code that jumps to the label is
contained within an @code{#ifdef} conditional. GNU C++ only permits
attributes on labels if the attribute specifier is immediately
@@ -4349,7 +4350,7 @@ attributes correctly apply to the declar
attributes the semantics this implies are not implemented.
When attribute specifiers follow the @code{*} of a pointer
declarator, they may be mixed with any type qualifiers present.
-The following describes the formal semantics of this syntax. It will make the
+The following describes the formal semantics of this syntax. It makes the
most sense if you are familiar with the formal specification of
declarators in the ISO C standard.
@@ -4397,18 +4398,18 @@ is not yet supported.
For compatibility with existing code written for compiler versions that
did not implement attributes on nested declarators, some laxity is
allowed in the placing of attributes. If an attribute that only applies
-to types is applied to a declaration, it will be treated as applying to
+to types is applied to a declaration, it is treated as applying to
the type of that declaration. If an attribute that only applies to
-declarations is applied to the type of a declaration, it will be treated
+declarations is applied to the type of a declaration, it is treated
as applying to that declaration; and, for compatibility with code
placing the attributes immediately before the identifier declared, such
-an attribute applied to a function return type will be treated as
+an attribute applied to a function return type is treated as
applying to the function type, and such an attribute applied to an array
-element type will be treated as applying to the array type. If an
+element type is treated as applying to the array type. If an
attribute that only applies to function types is applied to a
-pointer-to-function type, it will be treated as applying to the pointer
+pointer-to-function type, it is treated as applying to the pointer
target type; if such an attribute is applied to a function return type
-that is not a pointer-to-function type, it will be treated as applying
+that is not a pointer-to-function type, it is treated as applying
to the function type.
@node Function Prototypes
@@ -4579,7 +4580,7 @@ When used on a struct, or struct member,
only increase the alignment; in order to decrease it, the @code{packed}
attribute must be specified as well. When used as part of a typedef, the
@code{aligned} attribute can both increase and decrease alignment, and
-specifying the @code{packed} attribute will generate a warning.
+specifying the @code{packed} attribute generates a warning.
Note that the effectiveness of @code{aligned} attributes may be limited
@@ -4587,7 +4588,7 @@ only able to arrange for variables to be
alignment. (For some linkers, the maximum supported alignment may
be very very small.) If your linker is only able to align variables
up to a maximum of 8 byte alignment, then specifying @code{aligned(16)}
-in an @code{__attribute__} will still only provide you with 8 byte
+in an @code{__attribute__} still only provides you with 8 byte
The @code{aligned} attribute can also be used for functions
@@ -4603,7 +4604,7 @@ a pointer to a type compatible with the
of the function (if any) is ignored.
If @option{-fexceptions} is enabled, then @var{cleanup_function}
-will be run during the stack unwinding that happens during the
+is run during the stack unwinding that happens during the
processing of the exception. Note that the @code{cleanup} attribute
does not allow the exception to be caught, only to perform an action.
It is undefined what happens if @var{cleanup_function} does not
@@ -4639,8 +4640,9 @@ extern int old_var;
int new_fn () @{ return old_var; @}
@end smallexample
-results in a warning on line 3 but not line 2. The optional msg
-argument, which must be a string, will be printed in the warning if
+@noindent
+results in a warning on line 3 but not line 2. The optional @var{msg}
+argument, which must be a string, is printed in the warning if
present.
The @code{deprecated} attribute can also be used for functions and
@@ -4720,7 +4722,7 @@ uninitialized global variables but the l
each object be defined once, with the exception that uninitialized
variables tentatively go in the @code{common} (or @code{bss}) section
and can be multiply defined''. Using the @code{section} attribute
-will change what section the variable goes into and may cause the
+changes what section the variable goes into and may cause the
linker to issue an error if an uninitialized variable has multiple
definitions. You can force a variable to be initialized with the
@option{-fno-common} flag or the @code{nocommon} attribute.
@@ -4770,7 +4772,7 @@ Not all targets support this attribute.
@item unused
This attribute, attached to a variable, means that the variable is meant
-to be possibly unused. GCC will not produce a warning for this
+to be possibly unused. GCC does not produce a warning for this
variable.
@item used
@@ -4778,7 +4780,7 @@ This attribute, attached to a variable,
emitted even if it appears that the variable is not referenced.
When applied to a static data member of a C++ class template, the
-attribute also means that the member will be instantiated if the
+attribute also means that the member is instantiated if the
class itself is instantiated.
@item vector_size (@var{bytes})
@@ -4792,7 +4794,7 @@ int foo __attribute__ ((vector_size (16)
@noindent
causes the compiler to set the mode for @code{foo}, to be 16 bytes,
divided into @code{int} sized units. Assuming a 32-bit int (a vector of
-4 units of 4 bytes), the corresponding mode of @code{foo} will be V4SI@.
+4 units of 4 bytes), the corresponding mode of @code{foo} is V4SI@.
This attribute is only applicable to integral and float scalars,
although arrays, pointers, and function return values are allowed in
@@ -4892,15 +4894,15 @@ Three attributes are currently defined f
@cindex @code{l1_data_A} variable attribute
@cindex @code{l1_data_B} variable attribute
Use these attributes on the Blackfin to place the variable into L1 Data SRAM.
-Variables with @code{l1_data} attribute will be put into the specific section
-named @code{.l1.data}. Those with @code{l1_data_A} attribute will be put into
+Variables with @code{l1_data} attribute are put into the specific section
+named @code{.l1.data}. Those with @code{l1_data_A} attribute are put into
the specific section named @code{.l1.data.A}. Those with @code{l1_data_B}
-attribute will be put into the specific section named @code{.l1.data.B}.
+attribute are put into the specific section named @code{.l1.data.B}.
@item l2
@cindex @code{l2} variable attribute
Use this attribute on the Blackfin to place the variable into L2 SRAM.
-Variables with @code{l2} attribute will be put into the specific section
+Variables with @code{l2} attribute are put into the specific section
named @code{.l2.data}.
@end table
@@ -4919,7 +4921,7 @@ Small model objects live in the lower 16
Medium and large model objects may live anywhere in the 32-bit address space
@end table
@@ -4938,8 +4940,8 @@ control bus which is specified with @cod
@table @code
@item based
-Any variable with the @code{based} attribute will be assigned to the
-@code{.based} section, and will be accessed with relative to the
+Any variable with the @code{based} attribute is assigned to the
+@code{.based} section, and is accessed with relative to the
@code{tp} register. @item tiny @@ -4963,7 +4965,7 @@ stored. Variables with the @code{io} attribute are used to address memory-mapped peripherals. If an address is specified, the variable is assigned that address, else it is not assigned an address (it is -assumed some other module will assign an address). Example: +assumed some other module assigns an address). Example: @example int timer_count __attribute__((io(0x123))); @@ -4995,7 +4997,7 @@ Two attributes are currently defined for If @code{packed} is used on a structure, or if bit-fields are used it may be that the Microsoft ABI packs them differently -than GCC would normally pack them. Particularly when moving packed +than GCC normally packs them. Particularly when moving packed data between functions compiled with GCC and the native Microsoft compiler (either via function call or as data in a file), it may be necessary to access either format. @@ -5034,8 +5036,8 @@ Handling of zero-length bitfields: MSVC interprets zero-length bitfields in the following ways: @enumerate -@item If a zero-length bitfield is inserted between two bitfields that would -normally be coalesced, the bitfields will not be coalesced. +@item If a zero-length bitfield is inserted between two bitfields that +are normally coalesced, the bitfields are not coalesced. For example: @@ -5048,12 +5050,12 @@ struct @} t1; @end smallexample -The size of @code{t1} would be 8 bytes with the zero-length bitfield. If the +The size of @code{t1} is 8 bytes with the zero-length bitfield. If the zero-length bitfield were removed, @code{t1}'s size would be 4 bytes. @item If a zero-length bitfield is inserted after a bitfield, @code{foo}, and the alignment of the zero-length bitfield is greater than the member that follows it, -@code{bar}, @code{bar} will be aligned as the type of the zero-length bitfield. +@code{bar}, @code{bar} is aligned as the type of the zero-length bitfield. For example: @@ -5073,9 +5075,9 @@ struct @} t3; @end smallexample -For @code{t2}, @code{bar} will be placed at offset 2, rather than offset 1. -Accordingly, the size of @code{t2} will be 4. For @code{t3}, the zero-length -bitfield will not affect the alignment of @code{bar} or, as a result, the size +For @code{t2}, @code{bar} is placed at offset 2, rather than offset 1. +Accordingly, the size of @code{t2} is 4. For @code{t3}, the zero-length +bitfield does not affect the alignment of @code{bar} or, as a result, the size of the structure. Taking this into account, it is important to note the following: @@ -5097,7 +5099,7 @@ struct @} t4; @end smallexample -Here, @code{t4} will take up 4 bytes. +Here, @code{t4} takes up 4 bytes. @end enumerate @item Zero-length bitfields following non-bitfield members are ignored: @@ -5111,7 +5113,7 @@ struct @} t5; @end smallexample -Here, @code{t5} will take up 2 bytes. +Here, @code{t5} takes up 2 bytes. @end enumerate @end table @@ -5142,8 +5144,8 @@ One attribute is currently defined for x @cindex @code{below100} attribute If a variable has the @code{below100} attribute (@code{BELOW100} is -allowed also), GCC will place the variable in the first 0x100 bytes of -memory and use special opcodes to access it. Such variables will be +allowed also), GCC places the variable in the first 0x100 bytes of +memory and use special opcodes to access it. Such variables are placed in either the @code{.bss_below100} section or the @code{.data_below100} section. @@ -5195,7 +5197,7 @@ typedef int more_aligned_int __attribute @noindent force the compiler to insure (as far as it can) that each variable whose -type is @code{struct S} or @code{more_aligned_int} will be allocated and +type is @code{struct S} or @code{more_aligned_int} is allocated and aligned @emph{at least} on a 8-byte boundary. On a SPARC, having all variables of type @code{struct S} aligned to 8-byte boundaries allows the compiler to use the @code{ldd} and @code{std} (doubleword load and @@ -5244,10 +5246,10 @@ objects of that type, the compiler's abi alignment is primarily useful only when you plan to create arrays of variables having the relevant (efficiently aligned) type. If you declare or use arrays of variables of an efficiently-aligned type, then -it is likely that your program will also be doing pointer arithmetic (or +it is likely that your program also does pointer arithmetic (or subscripting, which amounts to the same thing) on pointers to the relevant type, and the code that the compiler generates for these -pointer arithmetic operations will often be more efficient for +pointer arithmetic operations is often more efficient for efficiently-aligned types than for other types. The @code{aligned} attribute can only increase the alignment; but you @@ -5259,7 +5261,7 @@ only able to arrange for variables to be alignment. (For some linkers, the maximum supported alignment may be very very small.) If your linker is only able to align variables up to a maximum of 8 byte alignment, then specifying @code{aligned(16)} -in an @code{__attribute__} will still only provide you with 8 byte +in an @code{__attribute__} still only provides you with 8 byte alignment. See your linker documentation for further information. @item packed @@ -5278,7 +5280,7 @@ attribute on all @code{enum} definitions In the following example @code{struct my_packed_struct}'s members are packed closely together, but the internal layout of its @code{s} member -is not packed---to do that, @code{struct my_unpacked_struct} would need to +is not packed---to do that, @code{struct my_unpacked_struct} needs to be packed too. @smallexample @@ -5361,7 +5363,7 @@ pid_t wait (wait_status_ptr_t p) @item unused When attached to a type (including a @code{union} or a @code{struct}), this attribute means that variables of that type are meant to appear -possibly unused. GCC will not produce a warning for any variables of +possibly unused. GCC does not produce a warning for any variables of that type, even if the variable appears to do nothing. This is often the case with lock or thread classes, which are usually defined and then not referenced, but contain constructors and destructors that have @@ -5388,11 +5390,12 @@ typedef T1 T3 __attribute__ ((deprecated T3 z __attribute__ ((deprecated)); @end smallexample +@noindent results in a warning on line 2 and 3 but not lines 4, 5, or 6. No warning is issued for line 4 because T2 is not explicitly deprecated. Line 5 has no warning because T3 is explicitly -deprecated. Similarly for line 6. The optional msg -argument, which must be a string, will be printed in the warning if +deprecated. Similarly for line 6. The optional @var{msg} +argument, which must be a string, is printed in the warning if present. The @code{deprecated} attribute can also be used for functions and @@ -5445,7 +5448,7 @@ Note that the type visibility is applied associated with the class (vtable, typeinfo node, etc.). In particular, if a class is thrown as an exception in one shared object and caught in another, the class must have default visibility. -Otherwise the two shared objects will be unable to use the same +Otherwise the two shared objects are unable to use the same typeinfo node and exception handling will break. @end table @@ -5500,7 +5503,7 @@ Two attributes are currently defined for If @code{packed} is used on a structure, or if bit-fields are used it may be that the Microsoft ABI packs them differently -than GCC would normally pack them. Particularly when moving packed +than GCC normally packs them. Particularly when moving packed data between functions compiled with GCC and the native Microsoft compiler (either via function call or as data in a file), it may be necessary to access either format. @@ -5558,7 +5561,7 @@ designs, @code{__alignof__ (double)} is Some machines never actually require alignment; they allow reference to any data type even at an odd address. For these machines, @code{__alignof__} -reports the smallest alignment that GCC will give the data type, usually as +reports the smallest alignment that GCC gives the data type, usually as mandated by the target ABI. If the operand of @code{__alignof__} is an lvalue rather than a type, @@ -5658,8 +5661,8 @@ for inline substitution. Among these us alloca, use of variable sized data types (@pxref{Variable Length}), use of computed goto (@pxref{Labels as Values}), use of nonlocal goto, and nested functions (@pxref{Nested Functions}). Using @option{-Winline} -will warn when a function marked @code{inline} could not be substituted, -and will give the reason for the failure. +warns when a function marked @code{inline} could not be substituted, +and gives the reason for the failure. @cindex automatic @code{inline} for C++ member fns @cindex @code{inline} automatic for C++ member fns @@ -5700,8 +5703,8 @@ This combination of @code{inline} and @c effect of a macro. The way to use it is to put a function definition in a header file with these keywords, and put another copy of the definition (lacking @code{inline} and @code{extern}) in a library file. -The definition in the header file will cause most calls to the function -to be inlined. If any uses of the function remain, they will refer to +The definition in the header file causes most calls to the function +to be inlined. If any uses of the function remain, they refer to the single copy in the library. @node Volatiles @@ -5737,8 +5740,8 @@ vobj = 1; @end smallexample Unless @var{*ptr} and @var{vobj} can be aliased, it is not guaranteed -that the write to @var{*ptr} will have occurred by the time the update -of @var{vobj} has happened. If you need this guarantee, you must use +that the write to @var{*ptr} occurs by the time the update +of @var{vobj} happens. If you need this guarantee, you must use a stronger memory barrier such as: @smallexample @@ -5795,7 +5798,7 @@ access hardware. In an assembler instruction using @code{asm}, you can specify the operands of the instruction using C expressions. This means you need not -guess which registers or memory locations will contain the data you want +guess which registers or memory locations contain the data you want to use. You must specify an assembler instruction template much like what @@ -5857,10 +5860,10 @@ assembler input. The extended @code{asm machine instructions the compiler itself does not know exist. If the output expression cannot be directly addressed (for example, it is a bit-field), your constraint must allow a register. In that case, GCC -will use the register as the output of the @code{asm}, and then store +uses the register as the output of the @code{asm}, and then stores that register into the output. -The ordinary output operands must be write-only; GCC will assume that +The ordinary output operands must be write-only; GCC assumes that the values in these operands before the instruction are dead and need not be generated. Extended asm supports input-output or read-write operands. Use the constraint character @samp{+} to indicate such an @@ -5884,10 +5887,10 @@ The constraint @samp{"0"} for operand 1 same location as operand 0. A number in constraint is allowed only in an input operand and it must refer to an output operand. -Only a number in the constraint can guarantee that one operand will be in +Only a number in the constraint can guarantee that one operand is in the same place as another. The mere fact that @code{foo} is the value -of both operands is not enough to guarantee that they will be in the -same place in the generated assembler code. The following would not +of both operands is not enough to guarantee that they are in the +same place in the generated assembler code. The following does not work reliably: @smallexample @@ -5965,12 +5968,12 @@ have no part mentioned in the clobber de There is no way for you to specify that an input operand is modified without also specifying it as an output operand. Note that if all the output operands you specify are for this -purpose (and hence unused), you will then also need to specify +purpose (and hence unused), you then also need to specify @code{volatile} for the @code{asm} construct, as described below, to prevent GCC from deleting the @code{asm} statement as unused. If you refer to a particular hardware register from the assembler code, -you will probably have to list the register after the third colon to +you probably have to list the register after the third colon to tell the compiler the register's value is modified. In some assemblers, the register names begin with @samp{%}; to produce one @samp{%} in the assembler code, you must write @samp{%%} in the input. @@ -5984,9 +5987,9 @@ effect. But it is valid no matter what If your assembler instructions access memory in an unpredictable fashion, add @samp{memory} to the list of clobbered registers. This -will cause GCC to not keep memory values cached in registers across the +causes GCC to not keep memory values cached in registers across the assembler instruction and not optimize stores or loads to that memory. -You will also want to add the @code{volatile} keyword if the memory +You also should add the @code{volatile} keyword if the memory affected is not listed in the inputs or outputs of the @code{asm}, as the @samp{memory} clobber does not count as a side-effect of the @code{asm}. If you know how large the accessed memory is, you can add @@ -6020,7 +6023,7 @@ to break the line, plus a tab character assembler allows semicolons as a line-breaking character. Note that some assembler dialects use semicolons to start a comment. The input operands are guaranteed not to use any of the clobbered -registers, and neither will the output operands' addresses, so you can +registers, and neither do the output operands' addresses, so you can read and write the clobbered registers as many times as you like. Here is an example of multiple instructions in a template; it assumes the subroutine @code{_foo} accepts arguments in registers 9 and 10: @@ -6077,9 +6080,9 @@ arguments @code{x} which can convert aut Another way to make sure the instruction operates on the correct data type is to use a cast in the @code{asm}. This is different from using a variable @code{__arg} in that it converts more different types. For -example, if the desired type were @code{int}, casting the argument to -@code{int} would accept a pointer with no complaint, while assigning the -argument to an @code{int} variable named @code{__arg} would warn about +example, if the desired type is @code{int}, casting the argument to +@code{int} accepts a pointer with no complaint, while assigning the +argument to an @code{int} variable named @code{__arg} warns about using a pointer unless the caller explicitly casts it. If an @code{asm} has output operands, GCC assumes for optimization @@ -6106,9 +6109,9 @@ the @code{asm}. For example: @noindent The @code{volatile} keyword indicates that the instruction has -important side-effects. GCC will not delete a volatile @code{asm} if +important side-effects. GCC does not delete a volatile @code{asm} if it is reachable. (The instruction can still be deleted if GCC can -prove that control-flow will never reach the location of the +prove that control flow never reaches the location of the instruction.) Note that even a volatile @code{asm} instruction can be moved relative to other code, including across jump instructions. For example, on many targets there is a system @@ -6122,7 +6125,7 @@ setting it with a volatile @code{asm}, l @end smallexample @noindent -This will not work reliably, as the compiler may move the addition back +This does not work reliably, as the compiler may move the addition back before the volatile @code{asm}. To make it work you need to add an artificial dependency to the @code{asm} referencing a variable in the code you don't want moved, for example: @@ -6135,19 +6138,19 @@ you don't want moved, for example: Similarly, you can't expect a sequence of volatile @code{asm} instructions to remain perfectly consecutive. If you want consecutive output, use a single @code{asm}. -Also, GCC will perform some optimizations across a volatile @code{asm} +Also, GCC performs some optimizations across a volatile @code{asm} instruction; GCC does not forget everything'' when it encounters a volatile @code{asm} instruction the way some other compilers do. -An @code{asm} instruction without any output operands will be treated +An @code{asm} instruction without any output operands is treated identically to a volatile @code{asm} instruction. It is a natural idea to look for a way to give access to the condition code left by the assembler instruction. However, when we attempted to implement this, we found no way to make it work reliably. The problem -is that output operands might need reloading, which would result in +is that output operands might need reloading, which result in additional following store'' instructions. On most machines, these -instructions would alter the condition code before there was time to +instructions alter the condition code before there is time to test it. This problem doesn't arise for ordinary test'' and compare'' instructions because they don't have any output operands. @@ -6240,7 +6243,7 @@ However, we record the address of this @ address of a label that calls the @code{trace} function. This allows the @code{nop} instruction to be patched at runtime to be an unconditional branch to the stored label. It is assumed that an -optimizing compiler will move the labeled block out of line, to +optimizing compiler moves the labeled block out of line, to optimize the fall through path from the @code{asm}. If you are writing a header file that should be includable in ISO C @@ -6263,8 +6266,8 @@ Normally, GCC's estimate is perfectly ad code is generated, but it is possible to confuse the compiler if you use pseudo instructions or assembler macros that expand into multiple real instructions or if you use assembler directives that expand to more -space in the object file than would be needed for a single instruction. -If this happens then the assembler will produce a diagnostic saying that +space in the object file than is needed for a single instruction. +If this happens then the assembler produces a diagnostic saying that a label is unreachable. @subsection i386 floating point asm operands @@ -6304,7 +6307,7 @@ asm ("foo" : "=t" (a) : "f" (b)); This asm says that input B is not popped by the asm, and that the asm pushes a result onto the reg-stack, i.e., the stack is one deeper after the asm than it was before. But, it is possible that -reload will think that it can use the same reg for both the input and +reload thinks that it can use the same reg for both the input and the output, if input B dies in this insn. If any input operand uses the @code{f} constraint, all output reg @@ -6438,7 +6441,7 @@ to local register variables may be delet These local variables are sometimes convenient for use with the extended @code{asm} feature (@pxref{Extended Asm}), if you want to write one output of the assembler instruction directly into a particular register. -(This will work provided the register you specify fits the constraints +(This works provided the register you specify fits the constraints specified for that operand in the @code{asm}.) @end itemize @@ -6463,14 +6466,14 @@ Here @code{a5} is the name of the regist register which is normally saved and restored by function calls on your machine, so that library routines will not clobber it. -Naturally the register name is cpu-dependent, so you would need to +Naturally the register name is cpu-dependent, so you need to conditionalize your program according to cpu type. The register -@code{a5} would be a good choice on a 68000 for a variable of pointer +@code{a5} is a good choice on a 68000 for a variable of pointer type. On machines with register windows, be sure to choose a global'' register that is not affected magically by the function call mechanism. In addition, operating systems on one type of cpu may differ in how they -name the registers; then you would need additional conditionals. For +name the registers; then you need additional conditionals. For example, some 68000 operating systems call this register @code{%a5}. Eventually there may be a way of asking the compiler to choose a register @@ -6479,10 +6482,10 @@ how to enable you to guide the choice. Defining a global register variable in a certain register reserves that register entirely for this use, at least within the current compilation. -The register will not be allocated for any other purpose in the functions -in the current compilation. The register will not be saved and restored by +The register is not allocated for any other purpose in the functions +in the current compilation, and is not saved and restored by these functions. Stores into this register are never deleted even if they -would appear to be dead, but references may be deleted or moved or +appear to be dead, but references may be deleted or moved or simplified. It is not safe to access the global register variables from signal @@ -6493,8 +6496,8 @@ you recompile them specially for the tas @cindex @code{qsort}, and global register variables It is not safe for one function that uses a global register variable to call another such function @code{foo} by way of a third function -@code{lose} that was compiled without knowledge of this variable (i.e.@: in a -different source file in which the variable wasn't declared). This is +@code{lose} that is compiled without knowledge of this variable (i.e.@: in a +different source file in which the variable isn't declared). This is because @code{lose} might save the register and put some other value there. For example, you can't expect a global register variable to be available in the comparison-function that you pass to @code{qsort}, since @code{qsort} @@ -6503,7 +6506,7 @@ recompile @code{qsort} with the same glo solve this problem.) If you want to recompile @code{qsort} or other source files which do not -actually use your global register variable, so that they will not use that +actually use your global register variable, so that they do not use that register for any other purpose, then it suffices to specify the compiler option @option{-ffixed-@var{reg}}. You need not actually add a global register declaration to their source code. @@ -6520,13 +6523,13 @@ restore the value which belongs to its c @cindex value after @code{longjmp} @findex longjmp @findex setjmp -On most machines, @code{longjmp} will restore to each global register +On most machines, @code{longjmp} restores to each global register variable the value it had at the time of the @code{setjmp}. On some -machines, however, @code{longjmp} will not change the value of global +machines, however, @code{longjmp} does not change the value of global register variables. To be portable, the function that called @code{setjmp} should make other arrangements to save the values of the global register variables, and to restore them in a @code{longjmp}. This way, the same -thing will happen regardless of what @code{longjmp} does. +thing happens regardless of what @code{longjmp} does. All global register variable declarations must precede all function definitions. If such a declaration could appear after function @@ -6542,7 +6545,7 @@ as the subroutines for division and rema g2 are local temporaries. On the 68000, a2 @dots{} a5 should be suitable, as should d2 @dots{} d7. -Of course, it will not do to use more than a few of those. +Of course, it does not do to use more than a few of those. @node Local Reg Vars @subsection Specifying Registers for Local Variables @@ -6560,7 +6563,7 @@ register int *foo asm ("a5"); @noindent Here @code{a5} is the name of the register which should be used. Note that this is the same syntax used for defining global register -variables, but for a local variable it would appear within a function. +variables, but for a local variable it appears within a function. Naturally the register name is cpu-dependent, but this is not a problem, since specific registers are most often useful with explicit @@ -6569,18 +6572,18 @@ generally require that you conditionaliz cpu type. In addition, operating systems on one type of cpu may differ in how they -name the registers; then you would need additional conditionals. For +name the registers; then you need additional conditionals. For example, some 68000 operating systems call this register @code{%a5}. Defining such a register variable does not reserve the register; it remains available for other uses in places where flow control determines the variable's value is not live. -This option does not guarantee that GCC will generate code that has +This option does not guarantee that GCC generates code that has this variable in the register you specify at all times. You may not code an explicit reference to this register in the @emph{assembler -instruction template} part of an @code{asm} statement and assume it will -always refer to this variable. However, using the variable as an +instruction template} part of an @code{asm} statement and assume it +always refers to this variable. However, using the variable as an @code{asm} @emph{operand} guarantees that the specified register is used for the operand. @@ -6593,7 +6596,7 @@ register which is normally saved and res your machine, so that library routines will not clobber it. A common pitfall is to initialize multiple call-clobbered registers with arbitrary expressions, where a function call or library call for an -arithmetic operator will overwrite a register value from a previous +arithmetic operator overwrites a register value from a previous assignment, for example @code{r0} below: @smallexample register int *p1 asm ("r0") = @dots{}; @@ -6753,15 +6756,15 @@ one of its callers. The @var{level} arg scan up the call stack. A value of @code{0} yields the return address of the current function, a value of @code{1} yields the return address of the caller of the current function, and so forth. When inlining -the expected behavior is that the function will return the address of -the function that will be returned to. To work around this behavior use +the expected behavior is that the function returns the address of +the function that is returned to. To work around this behavior use the @code{noinline} function attribute. The @var{level} argument must be a constant integer. On some machines it may be impossible to determine the return address of any function other than the current one; in such cases, or when the top -of the stack has been reached, this function will return @code{0} or a +of the stack has been reached, this function returns @code{0} or a random value. In addition, @code{__builtin_frame_address} may be used to determine if the top of the stack has been reached. @@ -6799,12 +6802,12 @@ registers. The frame address is normall pushed on to the stack by the function. However, the exact definition depends upon the processor and the calling convention. If the processor has a dedicated frame pointer register, and the function has a frame, -then @code{__builtin_frame_address} will return the value of the frame +then @code{__builtin_frame_address} returns the value of the frame pointer register. On some machines it may be impossible to determine the frame address of any function other than the current one; in such cases, or when the top -of the stack has been reached, this function will return @code{0} if +of the stack has been reached, this function returns @code{0} if the first frame pointer is properly initialized by the startup code. This function should only be used with a nonzero argument for debugging @@ -6831,7 +6834,7 @@ the vector size for the variable, measur declaration above causes the compiler to set the mode for the @code{v4si} type to be 16 bytes wide and divided into @code{int} sized units. For a 32-bit @code{int} this means a vector of 4 units of 4 bytes, and the -corresponding mode of @code{foo} will be @acronym{V4SI}. +corresponding mode of @code{foo} is @acronym{V4SI}. The @code{vector_size} attribute is only applicable to integral and float scalars, although arrays, pointers, and function return values @@ -6844,20 +6847,20 @@ and as unsigned: @code{char}, @code{shor used to build floating-point vector types. Specifying a combination that is not valid for the current architecture -will cause GCC to synthesize the instructions using a narrower mode. +causes GCC to synthesize the instructions using a narrower mode. For example, if you specify a variable of type @code{V4SI} and your -architecture does not allow for this specific SIMD type, GCC will -produce code that uses 4 @code{SIs}. +architecture does not allow for this specific SIMD type, GCC +produces code that uses 4 @code{SIs}. The types defined in this manner can be used with a subset of normal C -operations. Currently, GCC will allow using the following operators +operations. Currently, GCC allows using the following operators on these types: @code{+, -, *, /, unary minus, ^, |, &, ~, %}@. The operations behave like C++ @code{valarrays}. Addition is defined as the addition of the corresponding elements of the operands. For -example, in the code below, each of the 4 elements in @var{a} will be +example, in the code below, each of the 4 elements in @var{a} is added to the corresponding 4 elements in @var{b} and the resulting -vector will be stored in @var{c}. +vector is stored in @var{c}. @smallexample typedef int v4si __attribute__ ((vector_size (16))); @@ -6880,9 +6883,9 @@ a1, @dots{}, an@} >> @{b0, b1, @dots{}, elements. For convenience, it is allowed to use a binary vector operation -where one operand is a scalar. In that case the compiler will transform +where one operand is a scalar. In that case the compiler transforms the scalar operand into a vector where each element is the scalar from -the operation. The transformation will happen only if the scalar could be +the operation. The transformation happens only if the scalar could be safely converted to the vector-element type. Consider the following code. @@ -7006,13 +7009,13 @@ they work on multiple types. The definition given in the Intel documentation allows only for the use of the types @code{int}, @code{long}, @code{long long} as well as their unsigned -counterparts. GCC will allow any integral scalar or pointer type that is +counterparts. GCC allows any integral scalar or pointer type that is 1, 2, 4 or 8 bytes in length. Not all operations are supported by all target processors. If a particular -operation cannot be implemented on the target processor, a warning will be -generated and a call an external function will be generated. The external -function will carry the same name as the builtin, with an additional suffix +operation cannot be implemented on the target processor, a warning is +generated and a call an external function is generated. The external +function carries the same name as the builtin, with an additional suffix @samp{_@var{n}} where @var{n} is the size of the data type. @c ??? Should we have a mechanism to suppress this warning? This is almost @@ -7020,8 +7023,8 @@ function will carry the same name as the @c mutex. In most cases, these builtins are considered a @dfn{full barrier}. That is, -no memory operand will be moved across the operation, either forward or -backward. Further, instructions will be issued as necessary to prevent the +no memory operand is moved across the operation, either forward or +backward. Further, instructions are issued as necessary to prevent the processor from speculating loads across the operation and from queuing stores after the operation. @@ -7091,7 +7094,7 @@ value of @code{*@var{ptr}} is @var{oldva @code{*@var{ptr}}. The bool'' version returns true if the comparison is successful and -@var{newval} was written. The val'' version returns the contents +@var{newval} is written. The val'' version returns the contents of @code{*@var{ptr}} before the operation. @item __sync_synchronize (...) @@ -7137,13 +7140,13 @@ functions, but all also have a memory mo identified by being prefixed with @samp{__atomic}, and most are overloaded such that they work with multiple types. -GCC will allow any integral scalar or pointer type that is 1, 2, 4, or 8 +GCC allows any integral scalar or pointer type that is 1, 2, 4, or 8 bytes in length. 16-byte integral types are also allowed if @samp{__int128} (@pxref{__int128}) is supported by the architecture. Target architectures are encouraged to provide their own patterns for each of these built-in functions. If no target is provided, the original -non-memory model set of @samp{__sync} atomic built-in functions will be +non-memory model set of @samp{__sync} atomic built-in functions are utilized, along with any required synchronization fences surrounding it in order to achieve the proper behaviour. Execution in this case is subject to the same restrictions as those built-in functions. @@ -7154,11 +7157,11 @@ to be resolved at runtime. The four non-arithmetic functions (load, store, exchange, and compare_exchange) all have a generic version as well. This generic -version will work on any data type. If the data type size maps to one +version works on any data type. If the data type size maps to one of the integral sizes which may have lock free support, the generic -version will utilize the lock free built-in function. Otherwise an -external call is left to be resolved at runtime. This external call will -be the same format with the addition of a @samp{size_t} parameter inserted +version utilizes the lock free built-in function. Otherwise an +external call is left to be resolved at runtime. This external call is +the same format with the addition of a @samp{size_t} parameter inserted as the first parameter indicating the size of the object being pointed to. All objects must be the same size. @@ -7194,20 +7197,20 @@ release stores in all threads. When implementing patterns for these built-in functions, the memory model parameter can be ignored as long as the pattern implements the most restrictive @code{__ATOMIC_SEQ_CST} model. Any of the other memory models -will execute correctly with this memory model but they may not execute as +execute correctly with this memory model but they may not execute as efficiently as they could with a more appropriate implemention of the relaxed requirements. Note that the C++11 standard allows for the memory model parameter to be determined at runtime rather than at compile time. These built-in -functions will map any runtime value to @code{__ATOMIC_SEQ_CST} rather +functions map any runtime value to @code{__ATOMIC_SEQ_CST} rather than invoke a runtime library call or inline a switch statement. This is standard compliant, safe, and the simplest approach for now. The memory model parameter is a signed int, but only the lower 8 bits are reserved for the memory model. The remainder of the signed int is reserved -for future use and should be 0. Use of the predefined atomic values will -ensure proper usage. +for future use and should be 0. Use of the predefined atomic values +ensures proper usage. @deftypefn {Built-in Function} @var{type} __atomic_load_n (@var{type} *ptr, int memmodel) This built-in function implements an atomic load operation. It returns the @@ -7220,7 +7223,7 @@ and @code{__ATOMIC_CONSUME}. @end deftypefn @deftypefn {Built-in Function} void __atomic_load (@var{type} *ptr, @var{type} *ret, int memmodel) -This is the generic version of an atomic load. It will return the +This is the generic version of an atomic load. It returns the contents of @code{*@var{ptr}} in @code{*@var{ret}}. @end deftypefn @@ -7235,7 +7238,7 @@ The valid memory model variants are @end deftypefn @deftypefn {Built-in Function} void __atomic_store (@var{type} *ptr, @var{type} *val, int memmodel) -This is the generic version of an atomic store. It will store the value +This is the generic version of an atomic store. It stores the value of @code{*@var{val}} into @code{*@var{ptr}}. @end deftypefn @@ -7252,9 +7255,9 @@ The valid memory model variants are @end deftypefn @deftypefn {Built-in Function} void __atomic_exchange (@var{type} *ptr, @var{type} *val, @var{type} *ret, int memmodel) -This is the generic version of an atomic exchange. It will store the +This is the generic version of an atomic exchange. It stores the contents of @code{*@var{val}} into @code{*@var{ptr}}. The original value -of @code{*@var{ptr}} will be copied into @code{*@var{ret}}. +of @code{*@var{ptr}} is copied into @code{*@var{ret}}. @end deftypefn @@ -7336,7 +7339,7 @@ All memory models are valid. @deftypefn {Built-in Function} void __atomic_clear (bool *ptr, int memmodel) This built-in function performs an atomic clear operation on -@code{*@var{ptr}}. After the operation, @code{*@var{ptr}} will contain 0. +@code{*@var{ptr}}. After the operation, @code{*@var{ptr}} contains 0. The valid memory model variants are @code{__ATOMIC_RELAXED}, @code{__ATOMIC_SEQ_CST}, and @@ -7364,7 +7367,7 @@ All memory orders are valid. @deftypefn {Built-in Function} bool __atomic_always_lock_free (size_t size, void *ptr) -This built-in function returns true if objects of @var{size} bytes will always +This built-in function returns true if objects of @var{size} bytes always generate lock free atomic instructions for the target architecture. @var{size} must resolve to a compile time constant and the result also resolves to compile time constant. @@ -7380,7 +7383,7 @@ if (_atomic_always_lock_free (sizeof (lo @deftypefn {Built-in Function} bool __atomic_is_lock_free (size_t size, void *ptr) -This built-in function returns true if objects of @var{size} bytes will always +This built-in function returns true if objects of @var{size} bytes always generate lock free atomic instructions for the target architecture. If it is not known to be lock free a call is made to a runtime routine named @code{__atomic_is_lock_free}. @@ -7520,8 +7523,8 @@ In addition to this, there are checking @code{__builtin___fprintf_chk} and @code{__builtin___vfprintf_chk}. These have just one additional argument, @var{flag}, right before format string @var{fmt}. If the compiler is able to optimize them to -@code{fputc} etc.@: functions, it will, otherwise the checking function -should be called and the @var{flag} argument passed to it. +@code{fputc} etc.@: functions, it does, otherwise the checking function +is called and the @var{flag} argument passed to it. @node Other Builtins @section Other built-in functions provided by GCC @@ -7921,7 +7924,7 @@ should be called and the @var{flag} argu GCC provides a large number of built-in functions other than the ones mentioned above. Some of these are for internal use in the processing -of exceptions or variable-length argument lists and will not be +of exceptions or variable-length argument lists and are not documented here because they may change from time to time; we do not recommend general use of these functions. @@ -7929,12 +7932,12 @@ The remaining functions are provided for @opindex fno-builtin GCC includes built-in versions of many of the functions in the standard -C library. The versions prefixed with @code{__builtin_} will always be +C library. The versions prefixed with @code{__builtin_} are always treated as having the same meaning as the C library function even if you specify the @option{-fno-builtin} option. (@pxref{C Dialect Options}) Many of these functions are only optimized in certain cases; if they are -not optimized in a particular case, a call to the library function will -be emitted. +not optimized in a particular case, a call to the library function is +emitted. @opindex ansi @opindex std @@ -8091,7 +8094,7 @@ type; this is what the C standard specif For example, @code{enum @{foo, bar@}} is not similar to @code{enum @{hot, dog@}}. -You would typically use this function in code whose execution varies +You typically use this function in code whose execution varies depending on the arguments' types. For example: @smallexample @@ -8124,7 +8127,7 @@ integer constant expression, is nonzero. This built-in function is analogous to the @samp{? :} operator in C, except that the expression returned has its type unaltered by promotion rules. Also, the built-in function does not evaluate the expression -that was not chosen. For example, if @var{const_exp} evaluates to true, +that is not chosen. For example, if @var{const_exp} evaluates to true, @var{exp2} is not evaluated even if it has side-effects. This built-in function can return an lvalue if the chosen argument is an @@ -8179,8 +8182,8 @@ return of 0 does not indicate that the v but merely that GCC cannot prove it is a constant with the specified value of the @option{-O} option. -You would typically use this function in an embedded application where -memory was a critical resource. If you have some complex calculation, +You typically use this function in an embedded application where +memory is a critical resource. If you have some complex calculation, you may want it to be folded if it involves constants, but need to call a function if it does not. For example: @@ -8192,9 +8195,9 @@ a function if it does not. For example: You may use this built-in function in either a macro or an inline function. However, if you use it in an inlined function and pass an -argument of the function as the argument to the built-in, GCC will -never return 1 when you call the inline function with a string constant -or compound literal (@pxref{Compound Literals}) and will not return 1 +argument of the function as the argument to the built-in, GCC +never returns 1 when you call the inline function with a string constant +or compound literal (@pxref{Compound Literals}) and does not return 1 when you pass a constant numeric value to the inline function unless you specify the @option{-O} option. @@ -8212,8 +8215,8 @@ static const int table[] = @{ This is an acceptable initializer even if @var{EXPRESSION} is not a constant expression, including the case where @code{__builtin_constant_p} returns 1 because @var{EXPRESSION} can be -folded to a constant but @var{EXPRESSION} contains operands that would -not otherwise be permitted in a static initializer (for example, +folded to a constant but @var{EXPRESSION} contains operands that are +not otherwise permitted in a static initializer (for example, @code{0 && foo ()}). GCC must be more conservative about evaluating the built-in in this case, because it has no opportunity to perform optimization. @@ -8242,7 +8245,7 @@ if (__builtin_expect (x, 0)) @end smallexample @noindent -would indicate that we do not expect to call @code{foo}, since +indicates that we do not expect to call @code{foo}, since we expect @code{x} to be zero. Since you are limited to integral expressions for @var{exp}, you should use constructions such as @@ -8269,10 +8272,10 @@ the program is undefined. It is useful compiler cannot deduce the unreachability of the code. One such case is immediately following an @code{asm} statement that -will either never terminate, or one that transfers control elsewhere +either never terminates, or one that transfers control elsewhere and never returns. In this example, without the -@code{__builtin_unreachable}, GCC would issue a warning that control -reaches the end of a non-void function. It would also generate code +@code{__builtin_unreachable}, GCC issues a warning that control +reaches the end of a non-void function. It also generates code to return after the @code{asm}. @smallexample @@ -8291,7 +8294,7 @@ int f (int c, int v) @end smallexample Because the @code{asm} statement unconditionally transfers control out -of the function, control will never reach the end of the function +of the function, control never reaches the end of the function body. The @code{__builtin_unreachable} is in fact unreachable and communicates this fact to the compiler. @@ -8373,7 +8376,7 @@ This function is used to minimize cache- a cache before it is accessed. You can insert calls to @code{__builtin_prefetch} into code for which you know addresses of data in memory that is likely to be accessed soon. -If the target supports them, data prefetch instructions will be generated. +If the target supports them, data prefetch instructions are generated. If the prefetch is done early enough before the access then the data will be in the cache by the time it is accessed. @@ -8402,8 +8405,8 @@ for (i = 0; i < n; i++) Data prefetch does not generate faults if @var{addr} is invalid, but the address expression itself must be valid. For example, a prefetch -of @code{p->next} will not fault if @code{p->next} is not a valid -address, but evaluation will fault if @code{p} is not a valid address. +of @code{p->next} does not fault if @code{p->next} is not a valid +address, but evaluation faults if @code{p} is not a valid address. If the target does not support data prefetch, the address expression is evaluated if it includes side effects but no other code is generated @@ -8464,7 +8467,7 @@ type is @code{long double}. @end deftypefn @deftypefn {Built-in Function} int __builtin_isinf_sign (...) -Similar to @code{isinf}, except the return value will be negative for +Similar to @code{isinf}, except the return value is negative for an argument of @code{-Inf}. Note while the parameter list is an ellipsis, this function only accepts exactly one floating point argument. GCC treats this parameter as type-generic, which means it @@ -9085,7 +9088,7 @@ FR-V instructions. They must be compile @code{acc} arguments are evaluated at compile time and specify the number of an accumulator register. For example, an @code{acc} argument of 2 -will select the ACC2 register. +selects the ACC2 register. @code{iacc} arguments are similar to @code{acc} arguments but specify the number of an IACC register. See @pxref{Other Built-in Functions} @@ -9453,7 +9456,7 @@ into the data cache. @item void __data_prefetch (const void *@var{x}) Use the @code{nldub} instruction to load the contents of address @var{x} -into the data cache. The instruction will be issued in slot I1@. +into the data cache. The instruction is issued in slot I1@. @end table @node X86 Built-in Functions @@ -9525,7 +9528,7 @@ check the target platform type. This function runs the CPU detection code to check the type of CPU and the features supported. This builtin needs to be invoked along with the builtins to check CPU type and features, @code{__builtin_cpu_is} and -@code{__builtin_cpu_supports}, only when used in a function that will be +@code{__builtin_cpu_supports}, only when used in a function that is executed before any constructors are called. The CPU detection code is automatically executed in a very high priority constructor. @@ -10854,8 +10857,8 @@ using the command-line option @option{-m The SCOUNT and POS bits of the DSP control register are global. The WRDSP, EXTPDP, EXTPDPV and MTHLIP instructions modify the SCOUNT and -POS bits. During optimization, the compiler will not delete these -instructions and it will not delete calls to functions containing +POS bits. During optimization, the compiler does not delete these +instructions and it does not delete calls to functions containing these instructions. At present, GCC only provides support for operations on 32-bit @@ -10889,8 +10892,8 @@ d = (v2q15) @{0.1234 * 0x1.0p15, 0.4567 @emph{Note:} The CPU's endianness determines the order in which values are packed. On little-endian targets, the first value is the least significant and the last value is the most significant. The opposite -order applies to big-endian targets. For example, the code above will -set the lowest byte of @code{a} to @code{1} on little-endian targets +order applies to big-endian targets. For example, the code above +sets the lowest byte of @code{a} to @code{1} on little-endian targets and @code{4} on big-endian targets. @emph{Note:} Q7, Q15 and Q31 values must be initialized with their integer @@ -10934,8 +10937,8 @@ typedef long long a64; @code{q31} and @code{i32} are actually the same as @code{int}, but we use @code{q31} to indicate a Q31 fractional value and @code{i32} to indicate a 32-bit integer value. Similarly, @code{a64} is the same as -@code{long long}, but we use @code{a64} to indicate values that will -be placed in one of the four DSP accumulators (@code{ac0},
+@code{long long}, but we use @code{a64} to indicate values that are
+placed in one of the four DSP accumulators (@code{$ac0}, @code{$ac1}, @code{$ac2} or @code{$ac3}).
Also, some built-in functions prefer or require immediate numbers as
@@ -11160,7 +11163,7 @@ b = (v2sf) @{e, f@};
the upper half of a register and which value is stored in the lower half.
On little-endian targets, the first value is the lower one and the second
value is the upper one. The opposite order applies to big-endian targets.
-For example, the code above will set the lower half of @code{a} to
+For example, the code above sets the lower half of @code{a} to
@code{1.5} on little-endian targets and @code{9.1} on big-endian targets.
@node MIPS Loongson Built-in Functions
@@ -11354,7 +11357,7 @@ Absolute value (@code{abs.ps}).
Align variable (@code{alnv.ps}).
@emph{Note:} The value of the third parameter must be 0 or 4
instruction description for details.
@end table
@@ -11597,7 +11600,7 @@ Saturating subtraction. Return the resu
@var{x}, storing the value @minus{}32768 if the result overflows.
@item void __builtin_halt (void)
-Halt. The processor will stop execution. This built-in is useful for
+Halt. The processor stops execution. This built-in is useful for
implementing assertions.
@end table
@@ -13697,10 +13700,10 @@ void vec_vsx_st (vector bool char, int,
void vec_vsx_st (vector bool char, int, signed char *);
@end smallexample
-Note that the @samp{vec_ld} and @samp{vec_st} builtins will always
+Note that the @samp{vec_ld} and @samp{vec_st} builtins always
generate the Altivec @samp{LVX} and @samp{STVX} instructions even
if the VSX instruction set is available. The @samp{vec_vsx_ld} and
-@samp{vec_vsx_st} builtins will always generate the VSX @samp{LXVD2X},
+@samp{vec_vsx_st} builtins always generate the VSX @samp{LXVD2X},
@samp{LXVW4X}, @samp{STXVD2X}, and @samp{STXVW4X} instructions.
@node SH Built-in Functions
@@ -13711,7 +13714,7 @@ families of processors:
@deftypefn {Built-in Function} {void} __builtin_set_thread_pointer (void *@var{ptr})
Sets the @samp{GBR} register to the specified value @var{ptr}. This is usually
used by system code that manages threads and execution contexts. The compiler
-normally will not generate code that modifies the contents of @samp{GBR} and
+normally does not generate code that modifies the contents of @samp{GBR} and
thus the value is preserved across function calls. Changing the @samp{GBR}
value in user code must be done with caution, since the compiler might use
@samp{GBR} in order to access thread local variables.
@@ -13720,7 +13723,7 @@ value in user code must be done with cau
@deftypefn {Built-in Function} {void *} __builtin_thread_pointer (void)
Returns the value that is currently set in the @samp{GBR} register.
turned into @samp{GBR} based displacement loads and stores, if possible.
For example:
@smallexample
@@ -14123,7 +14126,7 @@ void __tile_udn_send (unsigned long long
@end smallexample
The intrinsic @code{void __tile_network_barrier (void)} is used to
-guarantee that no network operatons before it will be reordered with
+guarantee that no network operations before it are reordered with
those after it.
@node TILEPro Built-in Functions
@@ -14160,7 +14163,7 @@ void __tile_udn_send (unsigned)
@end smallexample
The intrinsic @code{void __tile_network_barrier (void)} is used to
-guarantee that no network operatons before it will be reordered with
+guarantee that no network operations before it are reordered with
those after it.
@node Target Format Checks
@@ -14187,9 +14190,9 @@ bit-fields. See the Solaris man page fo
@subsection Darwin Format Checks
Darwin targets support the @code{CFString} (or @code{__CFString__}) in the format
-attribute context. Declarations made with such attribution will be parsed for correct syntax
+attribute context. Declarations made with such attribution are parsed for correct syntax
and format argument types. However, parsing of the format string itself is currently undefined
-and will not be carried out by this version of the compiler.
+and is not carried out by this version of the compiler.
also be used as format arguments. Note that the relevant headers are only likely to be
@@ -14326,7 +14329,7 @@ asm ("cpfoo %0" : "=B" (x));
@cindex pragma, disinterrupt
For the named functions, the compiler adds code to disable interrupts
for the duration of those functions. Any functions so named, which
-are not encountered in the source, cause a warning that the pragma was
+are not encountered in the source, cause a warning that the pragma is
not used. Examples:
@example
@@ -14398,7 +14401,7 @@ This pragma is accepted, but has no effe
@item unused (@var{var} [, @var{var}]@dots{})
@cindex pragma, unused
-This pragma declares variables to be possibly unused. GCC will not
+This pragma declares variables to be possibly unused. GCC does not
produce warnings for the listed variables. The effect is similar to
that of the @code{unused} attribute, except that this pragma may appear
anywhere within the variables' scopes.
@@ -14453,7 +14456,7 @@ Labels}).
This pragma gives the C function @var{oldname} the assembly symbol
@var{newname}. The preprocessor macro @code{__PRAGMA_REDEFINE_EXTNAME}
-will be defined if this pragma is available (currently on all platforms).
+is defined if this pragma is available (currently on all platforms).
@end table
This pragma and the asm labels extension interact in a complicated
@@ -14686,7 +14689,7 @@ push_macro} and restored by @code{#pragm
This pragma allows you to set target specific options for functions
defined later in the source file. One or more strings can be
-specified. Each function that is defined after this point will be as
+specified. Each function that is defined after this point is as
if @code{attribute((target("STRING")))} was specified for that
function. The parenthesis around the options is optional.
@@ -14703,7 +14706,7 @@ present, it is not implemented for other
This pragma allows you to set global optimization options for functions
defined later in the source file. One or more strings can be
-specified. Each function that is defined after this point will be as
+specified. Each function that is defined after this point is as
if @code{attribute((optimize("STRING")))} was specified for that
function. The parenthesis around the options is optional.
@@ -14762,7 +14765,7 @@ struct @{
@} foo;
@end smallexample
-In this example, the user would be able to access members of the unnamed
+In this example, you are able to access members of the unnamed
union with code like @samp{foo.b}. Note that only unnamed structs and
unions are allowed, you may not have, for example, an unnamed
@code{int}.
@@ -15178,8 +15181,8 @@ an rvalue.
G++ implements the same behavior as GCC does when assigning to a
volatile object -- there is no reread of the assigned-to object, the
assigned rvalue is reused. Note that in C++ assignment expressions
-are lvalues, and if used as an lvalue, the volatile object will be
-referred to. For instance, @var{vref} will refer to @var{vobj}, as
+are lvalues, and if used as an lvalue, the volatile object is
+referred to. For instance, @var{vref} refers to @var{vobj}, as
expected, in the following example:
@smallexample
@@ -15224,7 +15227,7 @@ void T::fn () __restrict__
@end smallexample
@noindent
-Within the body of @code{T::fn}, @var{this} will have the effective
+Within the body of @code{T::fn}, @var{this} has the effective
definition @code{T *__restrict__ const this}. Notice that the
interpretation of a @code{__restrict__} member function qualifier is
different to that of @code{const} or @code{volatile} qualifier, in that it
@@ -15254,7 +15257,7 @@ inlined, but sometimes an out-of-line co
of the function is taken or if inlining fails. In general, we emit an
out-of-line copy in all translation units where one is needed. As an
exception, we only emit inline virtual functions with the vtable, since
-it will always require a copy.
+it always requires a copy.
Local static variables and string constants used in an inline function
are also considered to have vague linkage, since they must be shared
@@ -15272,7 +15275,7 @@ and the vtable is only emitted in the tr
method is defined.
@emph{Note:} If the chosen key method is later defined as inline, the
-vtable will still be emitted in every translation unit which defines it.
+vtable is still emitted in every translation unit which defines it.
Make sure that any inline virtuals are declared inline in the class
body, even if they are not defined there.
@@ -15301,14 +15304,14 @@ these constructs will be discarded at li
COMDAT support.
On targets that don't support COMDAT, but do support weak symbols, GCC
-will use them. This way one copy will override all the others, but
-the unused copies will still take up space in the executable.
+uses them. This way one copy overrides all the others, but
+the unused copies still take up space in the executable.
For targets which do not support either COMDAT or weak symbols,
-most entities with vague linkage will be emitted as local symbols to
-avoid duplicate definition errors from the linker. This will not happen
-for local statics in inlines, however, as having multiple copies will
-almost certainly break things.
+most entities with vague linkage are emitted as local symbols to
+avoid duplicate definition errors from the linker. This does not happen
+for local statics in inlines, however, as having multiple copies
+almost certainly breaks things.
@xref{C++ Interface,,Declarations and Definitions in One Header}, for
another way to control placement of these constructs.
@@ -15345,9 +15348,9 @@ functions, debugging information, and th
virtual functions) must be kept in each object file that includes class
definitions. You can use this pragma to avoid such duplication. When a
header file containing @samp{#pragma interface} is included in a
-compilation, this auxiliary information will not be generated (unless
+compilation, this auxiliary information is not generated (unless
the main input source file itself uses @samp{#pragma implementation}).
-Instead, the object files will contain references to be resolved at link
time.
The second form of this directive is useful for the case where you have
@@ -15370,7 +15373,7 @@ implementation files.
If you use @samp{#pragma implementation} with no argument, it applies to
an include file with the same basename@footnote{A file's @dfn{basename}
-was the name stripped of all leading path information and of trailing
+is the name stripped of all leading path information and of trailing
suffixes, such as @samp{.h} or @samp{.C} or @samp{.cc}.} as your source
file. For example, in @file{allclass.cc}, giving just
@samp{#pragma implementation}
@@ -15411,7 +15414,7 @@ code for the function itself; this defin
that can be found via pointers (or by callers compiled without
inlining). If all calls to the function can be inlined, you can avoid
emitting the function by compiling with @option{-fno-implement-inlines}.
-If any calls were not inlined, you will get linker errors.
+If any calls are not inlined, you will get linker errors.
@node Template Instantiation
@section Where's the Template?
@@ -15467,18 +15470,18 @@ You have the following options for deali
@enumerate
@item
@opindex frepo
-Compile your template-using code with @option{-frepo}. The compiler will
-generate files with the extension @samp{.rpo} listing all of the
+Compile your template-using code with @option{-frepo}. The compiler
+generates files with the extension @samp{.rpo} listing all of the
template instantiations used in the corresponding object files which
-could be instantiated there; the link wrapper, @samp{collect2}, will
-then update the @samp{.rpo} files to tell the compiler where to place
+could be instantiated there; the link wrapper, @samp{collect2},
+then updates the @samp{.rpo} files to tell the compiler where to place
those instantiations and rebuild any affected object files. The
-will continue to place the instantiations in the same files.
+continues to place the instantiations in the same files.
This is your best option for application code written for the Borland
-model, as it will just work. Code written for the Cfront model will
-need to be modified so that the template definitions are available at
+model, as it just works. Code written for the Cfront model
+needs to be modified so that the template definitions are available at
one or more points of instantiation; usually this is as simple as adding
@code{#include <tmethods.cc>} to the end of each template header.
@@ -15541,8 +15544,8 @@ static template class Foo<int>;
@item
Do nothing. Pretend G++ does implement automatic instantiation
-management. Code written for the Borland model will work fine, but
-each translation unit will contain instances of each of the templates it
+management. Code written for the Borland model works fine, but
+each translation unit contains instances of each of the templates it
uses. In a large program, this can lead to an unacceptable amount of code
duplication.
@end enumerate
@@ -15563,7 +15566,7 @@ that is not an option, you can extract t
would be called for a given object/PMF pair and call it directly inside
the inner loop, to save a bit of time.
-Note that you will still be paying the penalty for the call through a
+Note that you still pay the penalty for the call through a
function pointer; on most modern architectures, such a call defeats the
branch prediction features of the CPU@. This is also true of normal
virtual function calls.
@@ -15609,7 +15612,7 @@ a constant integral expression currently
inclusive. Lower numbers indicate a higher priority.
In the following example, @code{A} would normally be created before
-@code{B}, but the @code{init_priority} attribute has reversed that order:
+@code{B}, but the @code{init_priority} attribute reverses that order:
@smallexample
Some_Class A __attribute__ ((init_priority (2000)));
@@ -15625,7 +15628,7 @@ relative ordering.
This type attribute informs C++ that the class is a Java interface. It may
only be applied to classes declared within an @code{extern "Java"} block.
-Calls to methods declared in this interface will be dispatched using GCJ's
+Calls to methods declared in this interface are dispatched using GCJ's
interface table mechanism, instead of regular virtual table dispatch.
@end table
@@ -15817,10 +15820,10 @@ an enumeration type ([dcl.enum]).
@section Java Exceptions
The Java language uses a slightly different exception handling model
-from C++. Normally, GNU C++ will automatically detect when you are
+from C++. Normally, GNU C++ automatically detects when you are
writing C++ code that uses Java exceptions, and handle them
appropriately. However, if C++ code only needs to execute destructors
-when Java exceptions are thrown through it, GCC will guess incorrectly.
+when Java exceptions are thrown through it, GCC guesses incorrectly.
Sample problematic code is:
@smallexample
@@ -15939,6 +15942,6 @@ variable is accessed outside the for sco
Old C system header files did not contain an @code{extern "C" @{@dots{}@}}
scope to set the language. On such systems, all header files are
implicitly scoped inside a C language scope. Also, an empty prototype
-@code{()} will be treated as an unspecified number of arguments, rather
+@code{()} is treated as an unspecified number of arguments, rather
than no arguments, as C++ demands.
@end table
|
2015-07-29 22:29:14
|
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|
https://zenodo.org/record/5543225/export/xd
|
Journal article Open Access
# An Empirical Study on Users' Perception Towards E-Learning Platforms
Smitha Sambrani
### Dublin Core Export
<?xml version='1.0' encoding='utf-8'?>
<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:contributor>Blue Eyes Intelligence Engineering and Sciences Publication(BEIESP)</dc:contributor>
<dc:creator>Smitha Sambrani</dc:creator>
<dc:date>2021-09-30</dc:date>
<dc:description>The current scenario e-learning approach got prominence during the covid-19 pandemic. Many institutions were greatly dependent on e-learning platforms like Edx, Coursera, Udemy, Swayam, Webex, Zoom, Google meet etc. to teach their students and also it became a major part of the education system. The purpose of the study is to identify the perception of learners and accordingly suggest faculty community and technology developing companies. In this context, the current study aims to measure the learners' perception towards e-learning with five dimensions are Usefulness, Ease-of-Use, Self-Efficacy, Attitude & Intention to Use, especially to measure at capital city of Telangana, namely Hyderabad. The learners' awareness of e-learning platforms is also examined along with the above variables. The hypothesis of the study is only one, 'which is there is no significance of users' perception found towards Usefulness, Ease-of-Use, Self-Efficacy, Attitude & Intention to Use etc. aspects of electronic Learning Approach’. Research has been carried out as a descriptive study basing on primary and secondary data sources and also with the help of a structured questionnaire, 121 learners have been examined. These learners are identified based on their availability and conducted a structured interview, in some cases its telephone interview and mail response. Thirty research articles were reviewed in the construction of a theoretical framework. To collect the responses, the convenience non-random sampling technique was used and has applied both the descriptive statistics and t-test to analyze data. The greater part of responders felt it is more useful, easy to use, it improves self-efficacy; they also have shown a positive attitude towards the e-learning approach. A high level of intention is shown towards the e-learning approach and platforms.</dc:description>
<dc:identifier>https://zenodo.org/record/5543225</dc:identifier>
<dc:identifier>10.35940/ijmh.L1367.096121</dc:identifier>
<dc:identifier>oai:zenodo.org:5543225</dc:identifier>
<dc:language>eng</dc:language>
<dc:relation>issn:2394-0913</dc:relation>
<dc:relation>url:https://zenodo.org/communities/covid-19</dc:relation>
<dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
<dc:source>International Journal of Management and Humanities (IJMH) 6(1) 31-34</dc:source>
<dc:subject>Learners' Perception, E-Learning, e-Learning Platforms</dc:subject>
<dc:subject>ISSN</dc:subject>
<dc:subject>Retrieval Number</dc:subject>
<dc:title>An Empirical Study on Users' Perception Towards E-Learning Platforms</dc:title>
<dc:type>info:eu-repo/semantics/article</dc:type>
<dc:type>publication-article</dc:type>
</oai_dc:dc>
26
10
views
|
2022-01-28 18:35:58
|
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|
https://ankursinha.in/2012/01/17/vim-classroom-for-beginners-repeat-for-apac.html
|
# ankursinha.in/blog
neuroscience/fedora/musings
Tue 17 January 2012
# VIM Classroom for beginners repeat for APAC
Posted by ankur in Tech (68 words, approximately a 1 minute read)
Hi there!
As promised, I'm going to repeat the VIM class for beginners tomorrow at 2100 IST (1530 UTC) to suit APAC. I'm going to cover more or less the same points I covered in the initial class. Please try and make it :)
The venue of course, is #fedora-classroom on Freenode.
To convert this time to your local time:
> date -d "Wed Jan 18 15:30:00 UTC 2012"
|
2022-05-24 19:36:06
|
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|
http://www.ck12.org/book/Basic-Speller-Student-Materials/r1/section/5.22/
|
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# 5.22: The Combinations [ur] and [ər]
Difficulty Level: At Grade Created by: CK-12
## The Combinations [ur] and [ər]
1. You can hear both of the combinations [ur] and [ər] in the word burner. Each of them combines a vowel with the sound of the <r>. They sound much alike, but one has strong stress and the other has weak stress.
In burner is the strong stress on the first vowel sound or is it on the second? ______.
The pronunciation of the vowel sound with strong stress in burner is written [ur]. The one with weak stress is written with a schwa: [ər]. We write the pronunciation of burner this way: [bu´\begin{align*}\acute{\text{u}}\end{align*}rnər].
2. Each of the following words contains the sound [ur]; none contains the sound [ər]. Mark the strong stress in each word and underline the letters that spell [ur] .
perchingcourageservicepurpose\begin{align*}& \text{perching} && \text{courage} && \text{service} && \text{purpose}\end{align*}
3. Each of the following words contains the sound [ər]; none contains [ur]. Mark the strong stress in each word and then underline the letters that spell [ər]:
centerdollarsdoctoreffort\begin{align*}& \text{center} && \text{dollars} && \text{doctor} && \text{effort}\end{align*}
4. Each of the following words contains either the sound [ur] or the sound [ər]. None of them contains both. Mark the strong stress in each word and underline the letters that spell the [ur] or the [ər]:
urgentcolorcirclesurface\begin{align*}& \text{urgent} && \text{color} && \text{circle} && \text{surface}\end{align*}
Which of the four words contains [ər]? ________________.
5. Each of the following words contains both [ur] and [ər]. Mark the strong stress in each word and underline the letters that spell [ər]:
searchermurderworkersmurmur\begin{align*}& \text{searcher} && \text{murder} && \text{workers} && \text{murmur}\end{align*}
Word Flow
In this Word Flow you can string together about one hundred words. Some will contain [ur]; some will contain [ur] and [ər]. If you can get more than fifty words, you are doing very well.
### Notes/Highlights Having trouble? Report an issue.
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2016-12-04 13:38:31
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|
http://vimhelp.appspot.com/os_win32.txt.html
|
Quick links: help overview · quick reference · user manual toc · reference manual toc · faq
os_win32.txt For Vim version 8.1. Last change: 2017 Mar 21
VIM REFERENCE MANUAL by George Reilly
win32 Win32 MS-Windows
This file documents the idiosyncrasies of the Win32 version of Vim.
The Win32 version of Vim works on Windows XP, Vista, 7, 8 and 10. There are
both console and GUI versions.
The 32 bit version also runs on 64 bit MS-Windows systems.
1. Known problems win32-problems
2. Startup win32-startup
3. Restore screen contents win32-restore
4. Using the mouse win32-mouse
5. Running under Windows 95 win32-win95
6. Running under Windows 3.1 win32-win3.1
7. Win32 mini FAQ win32-faq
Additionally, there are a number of common Win32 and DOS items:
File locations dos-locations
Using backslashes dos-backslash
Standard mappings dos-standard-mappings
Screen output and colors dos-colors
File formats dos-file-formats
:cd command dos-:cd
Interrupting dos-CTRL-Break
Temp files dos-temp-files
Shell option default dos-shell
Win32 GUI gui-w32
Credits:
The Win32 version was written by George V. Reilly <george@reilly.org>.
The original Windows NT port was done by Roger Knobbe <RogerK@wonderware.com>.
The GUI version was made by George V. Reilly and Robert Webb.
For compiling see "src/INSTALLpc.txt". win32-compiling
==============================================================================
1. Known problems win32-problems
When doing file name completion, Vim also finds matches for the short file
name. But Vim will still find and use the corresponding long file name. For
example, if you have the long file name "this_is_a_test" with the short file
name "this_i~1", the command ":e *1" will start editing "this_is_a_test".
==============================================================================
2. Startup win32-startup
Current directory win32-curdir
If Vim is started with a single file name argument, and it has a full path
(starts with "x:\"), Vim assumes it was started from the file explorer and
will set the current directory to where that file is. To avoid this when
typing a command to start Vim, use a forward slash instead of a backslash.
Example:
vim c:\text\files\foo.txt
Will change to the "C:\text\files" directory.
vim c:/text\files\foo.txt
Will use the current directory.
Term option win32-term
The only kind of terminal type that the Win32 version of Vim understands is
"win32", which is built-in. If you set 'term' to anything else, you will
probably get very strange behavior from Vim. Therefore Vim does not obtain
the default value of 'term' from the environment variable "TERM".
$PATH win32-PATH The directory of the Vim executable is appended to$PATH. This is mostly to
make "!xxd" work, as it is in the Tools menu. And it also means that when
executable() returns 1 the executable can actually be executed.
Command line arguments win32-cmdargs
Analysis of a command line into parameters is not standardised in MS Windows.
Vim and gvim used to use different logic to parse it (before 7.4.432), and the
logic was also depended on what it was compiled with. Now Vim and gvim both
use the CommandLineToArgvW() Win32 API, so they behave in the same way.
The basic rules are: win32-backslashes
a) A parameter is a sequence of graphic characters.
b) Parameters are separated by white space.
c) A parameter can be enclosed in double quotes to include white space.
d) A sequence of zero or more backslashes (\) and a double quote (")
is special. The effective number of backslashes is halved, rounded
down. An even number of backslashes reverses the acceptability of
spaces and tabs, an odd number of backslashes produces a literal
double quote.
So:
" is a special double quote
\" is a literal double quote
\\" is a literal backslash and a special double quote
\\\" is a literal backslash and a literal double quote
\\\\" is 2 literal backslashes and a special double quote
\\\\\" is 2 literal backslashes and a literal double quote
etc.
Example:
vim "C:\My Music\freude" +"set ignorecase" +/"\"foo\\" +\"bar\\\"
opens "C:\My Music\freude" and executes the line mode commands:
set ignorecase; /"foo\ and /bar\"
These rules are also described in the reference of the CommandLineToArgvW API:
https://msdn.microsoft.com/en-us/library/windows/desktop/bb776391.aspx
win32-quotes
There are additional rules for quotes (which are not well documented).
As described above, quotes inside a file name (or any other command line
argument) can be escaped with a backslash. E.g.
vim -c "echo 'foo\"bar'"
Alternatively use three quotes to get one:
vim -c "echo 'foo"""bar'"
The quotation rules are:
1. A " starts quotation.
2. Another " or "" ends quotation. If the quotation ends with "", a "
is produced at the end of the quoted string.
Examples, with [] around an argument:
"foo" -> [foo]
"foo"" -> [foo"]
"foo"bar -> [foobar]
"foo" bar -> [foo], [bar]
"foo""bar -> [foo"bar]
"foo"" bar -> [foo"], [bar]
"foo"""bar" -> [foo"bar]
==============================================================================
3. Restore screen contents win32-restore
When 'restorescreen' is set (which is the default), Vim will restore the
original contents of the console when exiting or when executing external
commands. If you don't want this, use ":set nors". 'restorescreen'
==============================================================================
4. Using the mouse win32-mouse
The Win32 version of Vim supports using the mouse. If you have a two-button
mouse, the middle button can be emulated by pressing both left and right
buttons simultaneously - but note that in the Win32 GUI, if you have the right
mouse button pop-up menu enabled (see 'mouse'), you should err on the side of
pressing the left button first. mouse-using
When the mouse doesn't work, try disabling the "Quick Edit Mode" feature of
the console.
==============================================================================
5. Running under Windows 95 win32-win95
windows95 windows98 windowsme
Windows 95/98/ME support was removed in patch 8.0.0029 If you want to use it
you will need to get a version older than that.
==============================================================================
6. Running under Windows 3.1 win32-win3.1
win32s windows-3.1 gui-w32s win16
There was a special version of gvim that runs under Windows 3.1 and 3.11.
Support was removed in patch 7.4.1363.
==============================================================================
7. Win32 mini FAQ win32-faq
Q. How do I change the font?
A. In the GUI version, you can use the 'guifont' option. Example:
:set guifont=Lucida_Console:h15:cDEFAULT
In the console version, you need to set the font of the console itself.
You cannot do this from within Vim.
Q. How do I type dead keys on Windows NT?
A. Dead keys work on NT 3.51. Just type them as you would in any other
application.
On NT 4.0, you need to make sure that the default locale (set in the
Keyboard part of the Control Panel) is the same as the currently active
locale. Otherwise the NT code will get confused and crash! This is a NT
4.0 problem, not really a Vim problem.
Q. I'm using Vim to edit a symbolically linked file on a Unix NFS file server.
When I write the file, Vim does not "write through" the symlink. Instead,
it deletes the symbolic link and creates a new file in its place. Why?
A. On Unix, Vim is prepared for links (symbolic or hard). A backup copy of
the original file is made and then the original file is overwritten. This
assures that all properties of the file remain the same. On non-Unix
systems, the original file is renamed and a new file is written. Only the
protection bits are set like the original file. However, this doesn't work
properly when working on an NFS-mounted file system where links and other
things exist. The only way to fix this in the current version is not
making a backup file, by ":set nobackup nowritebackup" 'writebackup'
Q. I'm using Vim to edit a file on a Unix file server through Samba. When I
write the file, the owner of the file is changed. Why?
A. When writing a file Vim renames the original file, this is a backup (in
case writing the file fails halfway). Then the file is written as a new
file. Samba then gives it the default owner for the file system, which may
differ from the original owner.
To avoid this set the 'backupcopy' option to "yes". Vim will then make a
copy of the file for the backup, and overwrite the original file. The
owner isn't changed then.
Q. How do I get to see the output of ":make" while it's running?
A. Basically what you need is to put a tee program that will copy its input
(the output from make) to both stdout and to the errorfile. You can find a
copy of tee (and a number of other GNU tools) at
http://gnuwin32.sourceforge.net or http://unxutils.sourceforge.net
Alternatively, try the more recent Cygnus version of the GNU tools at
http://www.cygwin.com Other Unix-style tools for Win32 are listed at
When you do get a copy of tee, you'll need to add
:set shellpipe=\|\ tee
Q. I'm storing files on a remote machine that works with VisionFS, and files
disappear!
A. VisionFS can't handle certain dot (.) three letter extension file names.
SCO declares this behavior required for backwards compatibility with 16bit
DOS/Windows environments. The two commands below demonstrate the behavior:
echo Hello > file.bat~
dir > file.bat
The result is that the "dir" command updates the "file.bat~" file, instead
of creating a new "file.bat" file. This same behavior is exhibited in Vim
when editing an existing file named "foo.bat" because the default behavior
of Vim is to create a temporary file with a '~' character appended to the
name. When the file is written, it winds up being deleted.
:set backupext=.temporary
Q. How do I change the blink rate of the cursor?
A. You can't! This is a limitation of the NT console. NT 5.0 is reported to
be able to set the blink rate for all console windows at the same time.
:!start
Q. How can I asynchronously run an external command or program, or open a
document or URL with its default program?
A. When using :! to run an external command, you can run it with "start". For
To open "image.jpg" with the default image viewer:
:!start image.jpg
To open the folder of the current file in Windows Explorer:
:!start %:h
:!start http://www.vim.org/
Using "start" stops Vim switching to another screen, opening a new console,
or waiting for the program to complete; it indicates that you are running a
program that does not affect the files you are editing. Programs begun
with :!start do not get passed Vim's open file handles, which means they do
not have to be closed before Vim.
To avoid this special treatment, use ":! start".
There are two optional arguments (see the next Q):
/min the window will be minimized
/b no console window will be opened
You can use only one of these flags at a time. A second one will be
treated as the start of the command.
Q. How do I avoid getting a window for programs that I run asynchronously?
A. You have two possible solutions depending on what you want:
1) You may use the /min flag in order to run program in a minimized state
with no other changes. It will work equally for console and GUI
applications.
2) You can use the /b flag to run console applications without creating a
console window for them (GUI applications are not affected). But you
should use this flag only if the application you run doesn't require any
input. Otherwise it will get an EOF error because its input stream
(stdin) would be redirected to \\.\NUL (stdout and stderr too).
Example for a console application, run Exuberant ctags:
:!start /min ctags -R .
When it has finished you should see file named "tags" in your current
This is more noticeable for commands that take longer.
Now delete the "tags" file and run this command:
:!start /b ctags -R .
You should have the same "tags" file, but this time there will be no
Example for a GUI application:
|
2018-11-19 20:34:42
|
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|
http://www.scienceforums.net/topic/68505-why-do-we-use-n-1-for-sample-denominator/
|
# Why do we use n-1 for sample denominator?
## Recommended Posts
Hi.
So I understand the concept of degrees of freedom, as in we are not free to choose x many variables. Like if there are three numbers and the mean is 20, the degree of freedom is 2, because if we choose 2 numbers, the third one is defined.
I don't get, however, why sample's of a population use n-1 in the denominator, when populations only use 1.
Lets say this is a population: 1,3,5,2,7,8,6,9,2,7. The mean would be 50/10=5. The variance is 7.2.
Let's take a sample of this population. 5+7+6+8+7.
Let's take a sample of this population. 5+7+6+8+7. The mean would be 33/5=6.6. The variance, using N IN THE DENOMINATOR (which I know is incorrect), would be 1.04. With N-1 as the denominator, the answer is 1.3. I fail to see how 1.3 is any more accurate of the population than 1.04, since neither is anywhere close to 7.2. I guess because it is ever so slightly closer to 7.2?
I don't really get it conceptually.
Also, if the sample was 1,3,7,8,9. The mean would be 5.6. The variance using N would be 9.44. The variance using N-1 would be 11.8. So in this case, N is actually closer to the real deal of 7.2, than n-1 would be
##### Share on other sites
When using the standard formula for covariance with a sample the statistic is in fact biased due intuitively to the fact that the covariance depends upon the mean, which in turn depends on the sample. To correct this, and form an unbiased statistic we must multiple the standard formula for covariance by $\frac{N}{N-1}$. This is called Bessel's Correction.
##### Share on other sites
To add to what DJBruce said, as I understand it, the degrees of freedom is just that: the number of entries in the residuals vector that are 'allowed' to vary:
since the residuals, $(x_1 - \overline{x} ... x_n - \overline{x})$, must sum to zero, the entire vector is determined fully by the first N-1 entries.
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2018-01-22 20:26:44
|
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|
https://nrich.maths.org/4912
|
A Problem of Time
Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?
Eight Dominoes
Using the 8 dominoes make a square where each of the columns and rows adds up to 8
Holly
The ten arcs forming the edges of the "holly leaf" are all arcs of circles of radius 1 cm. Find the length of the perimeter of the holly leaf and the area of its surface.
A Roll of Patterned Paper
Stage: 4 Challenge Level:
In what follows I'm going to call the design above the "unit shape" and imagine it repeated endlessly along a line - rather like a stream of paper coming off a roll.
Here are two pieces from the roll :
The second piece has then been turned around (rotated 180 $^\circ$).
Try to design a new unit shape (probably simpler than mine) to make a strip which looks the same after a 180 $^\circ$ rotation.
In other words, make it so that you could not say whether the torn off strip had or had not been rotated.
There are two possibilities: across and along
First the original strip could have a mirror across it.
This illustration shows the right side as the reflection of the left side
Can you create a unit shape so that the strip has reflection symmetry across a vertical mirror line ?
And where would the mirror line need to be to be placed ?
Now try a mirror 'along' the torn off strip
The mirror could be reflecting the top half,
or (below) the bottom half.
Can you make a strip that has reflection symmetry across a horizontal mirror line ?
If you'd like more of this sort of thing, try the problem called 'One Reflection Implies Another'.
|
2017-11-19 02:52:07
|
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|
https://gmatclub.com/forum/toys4them-an-online-toy-merchant-generated-220-million-in-145880.html
|
GMAT Question of the Day - Daily to your Mailbox; hard ones only
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### Show Tags
16 Jan 2013, 14:21
1
1
00:00
Difficulty:
55% (hard)
Question Stats:
67% (01:38) correct 33% (01:29) wrong based on 522 sessions
### HideShow timer Statistics
Toys4Them, an online toy merchant, generated $220 million in revenue last year, an 8.6 percent increase over the previous year. However, the number of toys sold did not increase significantly last year over the previous year. Each of the following, if true, could explain the apparent discrepancy EXCEPT: a)Last year, Toys4Them changed its accounting policy to no longer count toys given away to charities as sold toys. b)Toys4Them sold a higher proportion of more expensive toys last year than the previous year. c)Last year, the number of consumers shopping for toys increased over the previous year. d)Last year, Toys4Them experienced an unprecedented boom in its divisions that do not sell toys. e)Because of an economic downturn, Toys4Them heavily discounted its toys during the holiday season two years ago. IMO , except C & E , all other options clearly resolve the discrepancy. OA is C not E. However I could nt be able to figure out , how does option E resolve the discrepancy . So help me to figure out the same ... Thanks in advance . Board of Directors Joined: 01 Sep 2010 Posts: 3291 Re: Toys4Them, an online toy merchant, generated$220 million in [#permalink]
### Show Tags
16 Jan 2013, 15:17
2
happy to clarify
When you deal with such question (indeed tough) try to understand really the argument.
Here we have an increase of revenue from one year to another year and a diminish of toys sold
E says that Toys4Them heavily discounted its toys during the holiday season two years ago (i.e 2012 during christmas holidays, could be an option) then the next year we have an increase of revenue BUT the toys are not purchased because people already have. May be they buy other stuffs from other compnany but not the same. As such, we end with more money in out bank account (the company) but with fewer toys sold.C instead, perfectly adheres to our case EXCEPT question
Plan B. always try to figure out a plane B, a second strategy to deal with because this exam is just this: seeing the things from an odd angle.
Even if you do not understand completely the stimulus (could happens) if you notice all options talk about toys $$BUT$$ only C talks about the number of consumers . We care about ONLY of toys $$NOT$$ consumers.
_________________
Intern
Joined: 01 Dec 2012
Posts: 33
Concentration: Finance, Operations
GPA: 2.9
### Show Tags
16 Jan 2013, 16:47
I'm not sure what you really mean
But I say do not infer too much. Never on GMAT. often students (me too) tend to see beyond the argument at stake. i.e if the discount is not present or offered
Stay in the "area" of the question. nothing more, nothing less.
Only in weaken or strengthen the argument almost always the time the answer is something out of scope, in somehow.
_________________
Manager
Joined: 04 Jan 2013
Posts: 71
Re: Toys4Them, an online toy merchant, generated $220 million in [#permalink] ### Show Tags 17 Jan 2013, 13:20 MOKSH wrote: Toys4Them, an online toy merchant, generated$220 million in revenue last year, an 8.6 percent increase over the previous year. However, the number of toys sold did not increase significantly last year over the previous year.
Each of the following, if true, could explain the apparent discrepancy EXCEPT:
a)Last year, Toys4Them changed its accounting policy to no longer count toys given away to charities as sold toys.
b)Toys4Them sold a higher proportion of more expensive toys last year than the previous year.
c)Last year, the number of consumers shopping for toys increased over the previous year.
d)Last year, Toys4Them experienced an unprecedented boom in its divisions that do not sell toys.
e)Because of an economic downturn, Toys4Them heavily discounted its toys during the holiday season two years ago.
IMO , except C & E , all other options clearly resolve the discrepancy.
OA is C not E. However I could nt be able to figure out , how does option E resolve the discrepancy .
So help me to figure out the same ...
oh well,i think the best thing is to understand the question stem,the stimulus,and the answer choices themselves..check this one out.the arguement presented to answer makes a comparison of sales made last with a previous year under certain conditions(unstated assumptions)which brought in a difference in revenue collected..now the question stem asks to provide an option that does not explain the discrepancy in the arguement..the discrepancy they are talking about it the more revenue thing when less toys are sold out..all options except C explain that descrepancy..C is contradictory to the statement(the number of toys sold did not increase significantly last year over the previous year.)in a way that it says that consumers increased in number inferring that they bought more of the toys from that shop..hence C is the answer to the question.
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Joined: 17 Jan 2013
Posts: 7
Re: Toys4Them, an online toy merchant, generated $220 million in [#permalink] ### Show Tags 17 Jan 2013, 13:55 1 Category : resolve the paradox. For Paradox questions the correct answer will actively resolve the paradox, that is, it will allow both sides to be factually correct and it will either explain how the situation came into being or add a piece of information that shows how the two ideas or occurrences can coexist. Because you are not seeking to disprove one side of the situation, you must select the answer choice that contains a possible cause of the situation. So, when examining answers, ask yourself if the answer choice could lead to the situation in the stimulus. If so, the answer is correct. If an answer supports or proves only one side of the paradox, that answer will be incorrect. The correct answer must show how both sides coexist. The following types of answers are incorrect: 1. Explains only one side of the paradox If an answer supports or proves only one side of the paradox, that answer will be incorrect. The correct answer must show how both sides coexist. 2. Similarities and differences If the stimulus contains a paradox where two items are similar, then an answer choice that explains a difference between the two cannot be correct. Conversely, if the stimulus contains a paradox where two items are different, then an answer choice that explains why the two are similar cannot be correct. In short, a similarity cannot explain a difference, and a difference cannot explain a similarity. Toys4Them, an online toy merchant, generated$220 million in revenue last year, an 8.6 percent increase over the previous year. However, the number of toys sold did not increase significantly last year over the previous year.
Each of the following, if true, could explain the apparent discrepancy EXCEPT:
There are no conclusion in paradox questions, so all we got are facts. Examine the facts very closely.
toys4Them, an online toy merchant, generated $220 million in revenue last year, an 8.6 percent increase over the previous year It tells about the revenue last year$220 million, an 8.6 percent increase over the previous year. Does not tell anything about operating cost or profit. However, the number of toys sold did not increase significantly last year over the previous year.
a)Last year, Toys4Them changed its accounting policy to no longer count toys given away to charities as sold toys.-- Fair enough, if previously they were counting charity toys as sold and accounting for its sale, then changing that policy will increase there revenues and will actively resolve the paradox.
b)Toys4Them sold a higher proportion of more expensive toys last year than the previous year. --- This resolves the paradox if last year they hold more expensive toys than previous year, the increase revenue could be explained given the fact the total number of toys sold did not increased.
c)Last year, the number of consumers shopping for toys increased over the previous year. --- hmnnn. Classic example of what i mentioned above.If an answer supports or proves only one side of the paradox, that answer will be incorrect. The correct answer must show how both sides coexist. This only explains what may have caused the increase in revenue but does not address the fact that number of toys sold did not increased significantly. Correct Answer
d)Last year, Toys4Them experienced an unprecedented boom in its divisions that do not sell toys. --- This again holds both side of the conversation. If this is true then the increased revenue could be from this division and not from the sale of the toys.
e)Because of an economic downturn, Toys4Them heavily discounted its toys during the holiday season two years ago--- This hold both side of the conversation. More revenue generated but not significant increase in the number of toys sold. So this indeed resolve the paradox.
Take Away:
Resolve the paradox only gives you facts and facts are indisputable. So any answer choice that validate one of the facts but invalidate another one is always going to be wrong.
Right answer should explain you how this situation came into existence.
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### Show Tags
17 Jan 2013, 14:32
@kingston..i think it wouldnt be proper if you call the answer choices facts..the answer choices remain as unstated assumptions as long as we assume them true inorder to resolve the paradox..the above arguement is paradoxical in a way that it suggests maxumum profit in few sold items, i.e toys..i am not disproving any of the arguement in the question stem but rather i qualified one of the arguement inorder of reaching the needed equillibrium..a good example is that of two girls with different weights on a seesaw..you wouldnt measure the same distance from the pivot or fulcrum to each sitting place but rather you might want to shift one of girls in the right place to maintain the proper balance and that exactly what i have done..thanks [/quote]
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Joined: 17 Jan 2013
Posts: 7
### Show Tags
02 Sep 2013, 19:26
Looks pretty straightforward to me.
Sales has gone down, and revenue gone up.
Possibilties ?
A. Direct increase in price (option B)
B. Previously selling at lower price( option E)
C. Any other factor that had increased revenue, not related to sales(option D)
D. Not counting few non billed items - no effect ( A)
Left is C, # of consumers has no bearing on # of toys they are buying.
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GMAT Date: 08-02-2013
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### Show Tags
03 Sep 2013, 23:33
MOKSH wrote:
Toys4Them, an online toy merchant, generated $220 million in revenue last year, an 8.6 percent increase over the previous year. However, the number of toys sold did not increase significantly last year over the previous year. Each of the following, if true, could explain the apparent discrepancy EXCEPT: a)Last year, Toys4Them changed its accounting policy to no longer count toys given away to charities as sold toys. b)Toys4Them sold a higher proportion of more expensive toys last year than the previous year. c)Last year, the number of consumers shopping for toys increased over the previous year. d)Last year, Toys4Them experienced an unprecedented boom in its divisions that do not sell toys. e)Because of an economic downturn, Toys4Them heavily discounted its toys during the holiday season two years ago. Thanks in advance . Question: which answer does not explain why revenue increased while toys sold stayed roughly the same? (A) changed accounting methods --> artificially increased revenue (b) more expensive toys were sold than cheap toys, total is still same --> increased revenue (c) more consumers bought toys --> increased toys sold --> conflicts with what paragraph explicitly says --> this is unhelpful and thus the answer (d) another department did well --> increased revenue (e) economic downturn two years ago --> sold their toys less two years ago --> this year, prices were back to normal --> increased revenue Board of Directors Joined: 17 Jul 2014 Posts: 2617 Location: United States (IL) Concentration: Finance, Economics GMAT 1: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) Re: Toys4Them, an online toy merchant, generated$220 million in [#permalink]
### Show Tags
30 Sep 2016, 06:45
MOKSH wrote:
Toys4Them, an online toy merchant, generated $220 million in revenue last year, an 8.6 percent increase over the previous year. However, the number of toys sold did not increase significantly last year over the previous year. Each of the following, if true, could explain the apparent discrepancy EXCEPT: a)Last year, Toys4Them changed its accounting policy to no longer count toys given away to charities as sold toys. b)Toys4Them sold a higher proportion of more expensive toys last year than the previous year. c)Last year, the number of consumers shopping for toys increased over the previous year. d)Last year, Toys4Them experienced an unprecedented boom in its divisions that do not sell toys. e)Because of an economic downturn, Toys4Them heavily discounted its toys during the holiday season two years ago. C for me. any other answer helps to explain the discrepancy. Intern Joined: 27 Jun 2015 Posts: 18 Re: Toys4Them, an online toy merchant, generated$220 million in [#permalink]
### Show Tags
30 Sep 2016, 22:47
I agree with C). Nevertheless I have a question how to eliminate A)
"a)Last year, Toys4Them changed its accounting policy to no longer count toys given away to charities as sold toys."
If the company does not account the toys given away to charities as sold toys then the revenue should be lower and not greater or?
Example:
Year 2000: Revenue = 220 Mio (including 10 Mio for toys given away to charities)
Year 2001: Revenue = 210 (new accounting approach without the 10 Mio )
Can me someone explain how this argument helps to clarify that the revenue increased?
Thank you!
Kind regards.
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### Show Tags
01 Oct 2016, 09:23
Got it, thank you sayantanc2k.
I only thought about the decrease in revenue because of the changed approach (not counting donated toys) and did not consider anymore that the question states that the revenue increased.
Thank you
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WE: Supply Chain Management (Manufacturing)
### Show Tags
28 Nov 2018, 10:10
MOKSH wrote:
Toys4Them, an online toy merchant, generated $220 million in revenue last year, an 8.6 percent increase over the previous year. However, the number of toys sold did not increase significantly last year over the previous year. Each of the following, if true, could explain the apparent discrepancy EXCEPT: a)Last year, Toys4Them changed its accounting policy to no longer count toys given away to charities as sold toys. b)Toys4Them sold a higher proportion of more expensive toys last year than the previous year. c)Last year, the number of consumers shopping for toys increased over the previous year. d)Last year, Toys4Them experienced an unprecedented boom in its divisions that do not sell toys. e)Because of an economic downturn, Toys4Them heavily discounted its toys during the holiday season two years ago. IMO , except C & E , all other options clearly resolve the discrepancy. OA is C not E. However I could nt be able to figure out , how does option E resolve the discrepancy . So help me to figure out the same ... Thanks in advance . This seems to be a very easy question : Stem : Toys4Them, an online toy merchant, generated$220 million in revenue last year, an 8.6 percent increase over the previous year. However, the number of toys sold did not increase significantly last year over the previous year.
Paradox is if the increase in sales is very less, how did the revenue shoot up by 8.6%.
Pre-thought : 1. Cost per toy has increased.
2. Even if the cost of toys is same, sale of Higher Cost toys is more than lower cost toys ultimately increasing average cost of toys.
3. There is some external source of income which has increased the revenue.
What else.....mmm...
4. Actual no. of toys sold may be higher and we have wrong figure of toys (weird but here it helps to resolve option A).
So, lets come to options now.
a)Last year, Toys4Them changed its accounting policy to no longer count toys given away to charities as sold toys.
Resembles with Pre-thought 4, the actual no. of toys sold (sold + given in charity) is more than last year similar to increase in revenue but we are not counting the number
of toys given to charity this year and hence relative to previous year we can't see the same change in the no. of toys.
b)Toys4Them sold a higher proportion of more expensive toys last year than the previous year.
Resembles Pre-thought 2, Since there is a sale of higher proportion of toys which is expensive so average cost shoot up leading to greater revenue.
c)Last year, the number of consumers shopping for toys increased over the previous year.
Not related to revenue of this company. If the number of consumers increased they should have bought more toys. This doesn't help us to resolve paradox.
d)Last year, Toys4Them experienced an unprecedented boom in its divisions that do not sell toys.
Resembles Pre-thought 3, Unprecented boom in other divisions, so revenue increased from there.
e)Because of an economic downturn, Toys4Them heavily discounted its toys during the holiday season two years ago.
Resembles Pre-thought 1, Ok last year it was discounted and hence price of toy was less. This year no discount and hence relatively price per toy is higher.
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2018-12-17 15:14:37
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https://www.prepanywhere.com/prep/textbooks/functions-11-mcgraw-workbook/chapters/chapter-5-trig-functions/materials/chapter-review
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Chapter Review
Chapter
Chapter 5
Section
Chapter Review
Solutions 15 Videos
Which of the following values do you expect to follow a periodic pattern? Justify your answer for each case
a) the distance from the centre as a grandfather clock pendulum swings back and forth
b) the cost of sending a package by courier. Which varies depending on the weight of the package
c) the value of a stock over a 1-year period
Q1
a) Sketch a periodic function, f(x), with a maximum value of 8, a minimum of -5, and a period of 3.
b) Select a value a for x, and determine f(a).
c) Determine two other values, b and c, such that f(a) = f(b) = f(c).
Q2
Copy and complete the table of values for y = sin 2x.
Q3a
Use the table values to sketch a graph of y = sin 2x. On the same set of axes, sketch a graph of y = sin x
Q3b
Compare the graphs in part b). Describe the similarities and differences.
Q3c
a) Predict what the graph of y = -csc x looks like. Use a table of values or technology to sketch the graph. Is your prediction correct?
b) Sketch the graph of y = csc x on the same set of axes.
c) Describe the similarities and differences between the graphs.
Q4
Write two equations, one in the form y = a sin kx and one in the form y = a cos [k(x - d)], to match the graph.
Q5
Write two equations, one in the form y = a cos kx and one in the form y = a sin[k(x - d)], to match the graph.
Q6
Determine the amplitude, the period, the phase shift, and the vertical shift of each function.
a) y = 5 sin [3(x - 40^{\circ})] + 6
b) y = \dfrac{1}{4} cos [4x + 400^{\circ}] - 2
c) y = -7 sin [\dfrac{2}{3}(x + 75^{\circ})] - 1
d) y = 0.4 cos [3.5(x - 60^{\circ})] + 5.6
Q7
a) Transform the graph of f(x) = sin x to g(x) = -7 sin[\dfrac{1}{2}(x- 30^{\circ})] + 1. Show each step in the transformation.
b) State the domain and range of f(x) and g(x).
Q8
a) Transform the graph of f(x) = cos x to g(x) = \dfrac{2}{3} cos[5(x + 28^{\circ})] - 4. Show each step in the transformation.
b) State the domain and range of f(x) and g(x).
Q9
Determine the equation of a sine function that represents the graph shown.
Q10a
Determine the equation of a cosine function that represents the graph.
Q10b
The table shows the mid-season high temperatures for winter, spring, summer, and fall over a 3-year period for a city in Ontario.
a) Use the table to determine a sinusoidal model for the mid-season high temperature.
b) Graph the points in the table on the same axes as your model to verify the fit.
c) Is the fit as you expect? Explain any discrepancies.
Coming Soon
Q11
During a 12-h period, the tides in one area of the Bay of Fundy cause the water level to rise to 6 m above average sea level and to fall 6 m below average sea level. The depth of the water at low tide is 2 m.
a) Suppose the water is at average sea level at midnight and the tide is coming in. Draw a graph that shows the height of the tide over a 24-h period. Explain how you obtained the graph.
b) Determine an equation that represents the tide for part a) using
i) a sine function
ii) a cosine function
c) Suppose the water is at average sea level at 3 am. and the tide is coming in. Write an equation that represents this new situation. Explain your reasoning.
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2021-08-03 16:06:45
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https://wiki.santafe.edu/index.php?title=Randomness,_Structure_and_Causality_-_Abstracts&diff=cur&oldid=38887
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# Difference between revisions of "Randomness, Structure and Causality - Abstracts"
### From Santa Fe Institute Events Wiki
A Geometric Approach to Complexity
Ay, Nihat (nay@mis.mpg.de)
SFI & Max Planck Institute
I discuss several complexity measures of random fields from a geometric perspective. Central to this approach is the notion of multi-information, a generalization of mutual information. As demonstrated by Amari, information geometry allows to decompose this measure in a natural way. In my talk I will show how this decomposition leads to a unifying scheme of various approaches to complexity. In particular, connections to the complexity measure of Tononi, Sporns, and Edelman and also to excess entropy (predictive information) can be established. In the second part of my talk, the interplay between complexity and causality (causality in Pearl's sense) will be discussed. A generalization of Reichenbach's common cause principle will play a central role in this regard.
Learning Out of Equilibrium
Bell, Tony (tony@salk.edu)
UC Berkeley
Inspired by new results in non-equilibrium statistical mechanics, we define a new kind of state-machine that can be used to model time series. The machine is deterministically coupled to the inputs unlike stochastic generative models like the Kalman filter and HMM’s. The likelihood in this case is shown to be a sum of local time likelihoods. We introduce a new concept, second-order-in-time stochastic gradient, which derives from the time derivative of the likelihood, showing that the latter decomposes into a ‘work’ term, a ‘heat’ term and a term describing time asymmetry in the state machine’s dynamics. This motivates the introduction of a new time-symmetric likelihood function for time series. Our central result is that the time derivative of this is an average sum of forward and backward time ‘work’ terms, in which all partition functions, which plague Dynamic Bayesian Networks, have cancelled out. We can now do tractable time series density estimation with arbitrary models, without sampling. This is a direct result of doing second-order-in-time learning with time-symmetric likelihoods. A model is proposed, based on parameterised energy-based Markovian kinetics, with the goal of learning (bio)chemical networks from data, and taking a step towards understanding molecular-level energy-based self-organisation.
Information Aggregation in Correlated Complex Systems and Optimal Estimation
Bettencourt, Luis (lmbettencourt@gmail.com)
SFI & LANL
Information is a peculiar quantity. Unlike matter and energy, which are conserved by the laws of physics, the aggregation of knowledge from many sources can in fact produce more information (synergy) or less (redundancy) than the sum of its parts, provided these sources are correlated. I discuss how the formal properties of information aggregation - expressed in information theoretic terms - provide a general window for explaining features of organization in several complex systems. I show under what circumstances collective coordination may pay off in stochastic search problems, how this can be used to estimate functional relations between neurons in living neural tissue and more generally how it may have implications for other network structures in social and biological systems.
To a Mathematical Theory of Evolution and Biological Creativity
Chaitin, Gregory (gjchaitin@gmail.com)
IBM Watson Research Center
We present an information-theoretic analysis of Darwin’s theory of evolution, modeled as a hill-climbing algorithm on a fitness landscape. Our space of possible organisms consists of computer programs, which are subjected to random mutations. We study the random walk of increasing fitness made by a single mutating organism. In two different models we are able to show that evolution will occur and to characterize the rate of evolutionary progress, i.e., the rate of biological creativity.
Framing Complexity PDF
Crutchfield, James (chaos@cse.ucdavis.edu)
SFI & UC Davis
Is there a theory of complex systems? And who should care, anyway?
The Vocabulary of Grammar-Based Codes and the Logical Consistency of Texts
Debowski, Lukasz (ldebowsk@ipipan.waw.pl)
We will present a new explanation for the distribution of words in natural language which is grounded in information theory and inspired by recent research in excess entropy. Namely, we will demonstrate a theorem with the following informal statement: If a text of length ${\displaystyle n}$ describes ${\displaystyle n^{\beta }}$ independent facts in a repetitive way then the text contains at least ${\displaystyle n^{\beta }/\log n}$ different words. In the formal statement, two modeling postulates are adopted. Firstly, the words are understood as nonterminal symbols of the shortest grammar-based encoding of the text. Secondly, the text is assumed to be emitted by a finite-energy strongly nonergodic source whereas the facts are binary IID variables predictable in a shift-invariant way. Besides the theorem, we will exhibit a few stochastic processes to which this and similar statements can be related.
Prediction, Retrodiction, and the Amount of Information Stored in the Present
Ellison, Christopher (cellison@cse.ucdavis.edu)
Complexity Sciences Center, UC Davis
We introduce an ambidextrous view of stochastic dynamical systems, comparing their forward-time and reverse-time representations and then integrating them into a single time-symmetric representation. The perspective is useful theoretically, computationally, and conceptually. Mathematically, we prove that the excess entropy--a familiar measure of organization in complex systems--is the mutual information not only between the past and future, but also between the predictive and retrodictive causal states. Practically, we exploit the connection between prediction and retrodiction to directly calculate the excess entropy. Conceptually, these lead one to discover new system invariants for stochastic dynamical systems: crypticity (information accessibility) and causal irreversibility. Ultimately, we introduce a time-symmetric representation that unifies all these quantities, compressing the two directional representations into one. The resulting compression offers a new conception of the amount of information stored in the present.
Complexity Measures and Frustration
Feldman, David (dave@hornacek.coa.edu)
College of the Atlantic
In this talk I will present some new results applying complexity measures to frustrated systems, and I will also comment on some frustrations I have about past and current work in complexity measures. I will conclude with a number of open questions and ideas for future research.
I will begin with a quick review of the excess entropy/predictive information and argue that it is a well understood and broadly applicable measure of complexity that allows for a comparison of information processing abilities among very different systems. The vehicle for this comparison is the complexity-entropy diagram, a scatter-plot of the entropy and excess entropy as model parameters are varied. This allows for a direct comparison in terms of the configurations' intrinsic information processing properties. To illustrate this point, I will show complexity-entropy diagrams for: 1D and 2D Ising models, 1D Cellular Automata, the logistic map, an ensemble of Markov chains, and an ensemble of epsilon-machines.
I will then present some new work in which a local form of the 2D excess entropy is calculated for a frustrated spin system. This allows one to see how information and memory are shared unevenly across the lattice as the system enters a glassy state. These results show that localised information theoretic complexity measures can be usefully applied to heterogeneous lattice systems. I will argue that local complexity measures for higher-dimensional and heterogeneous systems is a particularly fruitful area for future research.
Finally, I will conclude by remarking upon some of the areas of complexity-measure research that have been sources of frustration. These include the persistent notions of a universal "complexity at the edge of chaos," and the relative lack of applications of complexity measures to empirical data and/or multidimensional systems. These remarks are designed to provoke dialog and discussion about interesting and fun areas for future research.
Links: Paper 1 and Paper 2
Introduction to the Workshop PDF
Complexity, Parallel Computation and Statistical Physics
Machta, Jon (machta@physics.umass.edu)
SFI & University of Massachusetts
In this talk I argue that a fundamental measure of physical complexity is obtained from the parallel computational complexity of sampling states of the system. After motivating this idea, I will briefly review relevant aspects of computational complexity theory, discuss the properties of the proposed measure of physical complexity and illustrate the ideas with some examples from statistical physics.
Crypticity and Information Accessibility
Mahoney, John (jmahoney3@ucmerced.edu)
UC Merced
We give a systematic expansion of the crypticity--a recently introduced measure of the inaccessibility of a stationary process's internal state information. This leads to a hierarchy of k-cryptic processes and allows us to identify finite-state processes that have infinite crypticity--the internal state information is present across arbitrarily long, observed sequences. The crypticity expansion is exact in both the finite- and infinite-order cases. It turns out that k-crypticity is complementary to the Markovian finite-order property that describes state information in processes. One application of these results is an efficient expansion of the excess entropy--the mutual information between a process's infinite past and infinite future--that is finite and exact for finite-order cryptic processes.
Automatic Identification of Information-Processing Structures in Cellular Automata
Mitchell, Melanie (mm@cs.pdx.edu)
SFI & Portland State University
Cellular automata have been widely used as idealized models of natural spatially-extended dynamical systems. An open question is how to best understand such systems in terms of their information-processing capabilities. In this talk we address this question by describing several approaches to automatically identifying the structures underlying information processing in cellular automata. In particular, we review the computational mechanics methods of Crutchfield et al., the local sensitivity and local statistical complexity filters proposed by Shalizi et al., and the information theoretic filters proposed by Lizier et al. We illustrate these methods by applying them to several one- and two-dimensional cellular automata that have been designed to perform the so-called density (or majority) classification task.
Phase Transitions and Computational Complexity
Moore, Cris (moore@cs.unm.edu)
SFI & University of New Mexico
A review and commentary on the fundamental concepts of computational complexity, beyond the usual discussion of P, NP and NP-completeness, in an attempt to explain the deep meaning of the P vs. NP question. I'll discuss counting, randomized algorithms, and higher complexity classes, and several topics that are current hotbeds of interdisciplinary research, like phase transitions in computation, Monte Carlo algorithms, and quantum computing.
Dominos, Ergodic Flows
Shaw, Rob (rob@protolife.net)
ProtoLife, Inc.
We present a model, developed with Norman Packard, of a simple discrete open flow system. Dimers are created at one edge of a two-dimensional lattice, diffuse across, and are removed at the opposite side. A steady-state flow is established, under various kinetic rules. In the equilibrium case, the system reduces to the classical monomer-dimer tiling problem, whose entropy as a function of density is known. This entropy density is reproduced locally in the flow system, as shown by statistics over local templates. The goal is to clarify informational aspects of a flowing pattern.
Statistical Mechanics of Interactive Learning
Still, Suzanne (sstill@hawaii.edu)
University of Hawaii at Manoa
The principles of statistical mechanics and information theory play an important role in learning and have inspired both theory and the design of numerous machine learning algorithms. The new aspect in this paper is a focus on integrating feedback from the learner. A quantitative approach to interactive learning and adaptive behavior is proposed, integrating model- and decision-making into one theoretical framework. This paper follows simple principles by requiring that the observer’s world model and action policy should result in maximal predictive power at minimal complexity. Classes of optimal action policies and of optimal models are derived from an objective function that reflects this trade-off between prediction and complexity. The resulting optimal models then summarize, at different levels of abstraction, the process’s causal organization in the presence of the learner’s actions. A fundamental consequence of the proposed principle is that the learner’s optimal action policies balance exploration and control as an emerging property. Interestingly, the explorative component is present in the absence of policy randomness, i.e. in the optimal deterministic behavior. This is a direct result of requiring maximal predictive power in the presence of feedback.
Ergodic Parameters and Dynamical Complexity PDF
Vilela-Mendes, Rui (vilela@cii.fc.ul.pt)
University of Lisbon
Using a cocycle formulation, old and new ergodic parameters beyond the Lyapunov exponent are rigorously characterized. Dynamical Renyi entropies and fluctuations of the local expansion rate are related by a generalization of the Pesin formula. How the ergodic parameters may be used to characterize the complexity of dynamical systems is illustrated by some examples: Clustering and synchronization, self-organized criticality and the topological structure of networks.
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2022-01-26 13:45:06
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http://tex.stackexchange.com/questions/47285/listings-with-rule-above-caption-to-look-like-floatstyleruled
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# Listings with rule above caption to look like \floatstyle{ruled}
I am using the listings package.
I would like my listings to have a heavy rule above the caption, so it looks like the \floatstyle{ruled}.
So it would look like:
a bold line ===
caption
rule ---
code
rule ---
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## migrated from stackoverflow.comMar 8 '12 at 17:16
This question came from our site for professional and enthusiast programmers.
Give a example file. I will give a solution – Mu30 Mar 9 '12 at 14:28
Welcome to TeX.SE. Please keep in mind that it is always best to compose a fully compilable MWE that illustrates the problem including the \documentclass and the appropriate packages so that those trying to help don't have to recreate it. Basically, show some work by getting the example as far as you can. – Peter Grill Mar 10 '12 at 3:59
The packages listings provides the option frame=single which draws a single line above and below the environment itself. So you have to add a single bold line before the caption is set. Therefore I am using the command pretocmd provided by etoolbox.
\documentclass{article}
\usepackage{listings}
\usepackage{etoolbox}
\makeatletter
\lstset{frame=lines}
\pretocmd\lst@makecaption{\noindent{\rule{\linewidth}{2pt}}}{}{}
\makeatother
\begin{document}
\begin{lstlisting}[caption={Some Caption}]
static uint64_t i = 0;
void every_cycle()
{
if (i > 0)
i--;
}
uint64_t next_num()
{
return (i += 0x100);
}
\end{lstlisting}
Text
\begin{lstlisting}
static uint64_t i = 0;
void every_cycle()
{
if (i > 0)
i--;
}
uint64_t next_num()
{
return (i += 0x100);
}
\end{lstlisting}
\end{document}
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2014-07-28 10:36:16
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https://astronomy.stackexchange.com/questions/28721/how-would-humans-with-appropriate-equipment-navigate-the-surface-of-saturns-moo
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# How would humans with appropriate equipment navigate the surface of Saturn's moon Titan on foot?
Taking into account the physical characteristics of Titan (e.g. surface gravity, atmospheric pressure), what would be the most efficient method of motion for an astronaut to navigate the surface of Titan on foot?
Would it be a leaping or hopping motion? Or would it make more sense to walk somehow? I'm unsure how the friction of the ground would accommodate for that.
For the purpose of this thought experiment, lets assume that humanity has the necessary equipment to put an astronaut on Titan and to have protective clothing to enable reasonable safety from environmental hazards on the surface.
• Could you add the details of Titan's characteristics that you have alluded to in the question? And for example, how do these compare to Earth or the Moon? – Mick Dec 14 '18 at 8:58
• The gravity is a comfortable 1.352 m/s2 (0.14 g in comparison with Earth) which equates to .85 Moons. The surface pressure is 146.7 kPa which compares to 1.45 atm (Earth). – Oak Dec 14 '18 at 10:23
• -1 It's generally discouraged to post the same question on more than one SE site at a time. It's called cross-posting. An important principle in Stack Exchange is to point people to the best answer. By generating two sets of answers on two sites, cross-posting tends to defeat this purpose and makes more work for others writing potentially duplicate answers. – uhoh Dec 15 '18 at 11:08
I wonder if this would be better for worldbuilding or space travel, but I can touch on the basics.
You'd need oxygen and protection from the cold, but a space suit on Titan would be less restrictive, not more restrictive than the ones used on the Moon. The pressure isn't too much, so that actually helps and cold temperature is much easier to protect from than a vacuum. They'd probably need some kind of full body wrap to avoid exposure and frostbite, and goggles but that's not terrible hard. Electric heating or just insulation would both be options.
But it's safe to assume that even if they carry an electric heating device, their suits would still be less bulky and less restrictive than the ones the astronauts wore on the Moon.
Hop or Walk?
Very likely hop. I'm going to borrow from this Quora answer, because I agree with it and it makes logical sense. Walking is kind of a controlled fall. Walking in 0.14 g, means your body doesn't fall forward in pace with every step, so walking would be weird and hoping would be easier.
Even on Mars, astronauts might hop due to the lower gravity. If I was to make a wild guess, for comfortable walking I think it would begin somewhere around 50% or 60% Earth gravity. Less then that, the slower rate of falling with each step and the lighter body weight, I think hopping is the way to go.
The human brain and inner ear begins to stop working somewhere around lunar gravity. There are videos of astronauts on the moon falling forward and looking clumsy, but they were very fit individuals. In low enough gravity the human brain loses a sense of which way is down. (I read that, I'll see if I can find a link).
I would think, if it was for an extended time there, astronauts on Titan would wear lead boots, to help with their sense of which way is down and also for helping maintain musculature, but that's just speculation on my part. There are other ways to maintain musculature.
Titan's surface might/probably gets soggy as well and humans aren't buoyant in methane lakes the way they are in water, (so maybe the lead boots aren't a good idea). Falling into a lake or falling through ice into a like might happen on titan, but they'd be wearing full body wraps and have oxygen, so falling into a methane lake wouldn't necessarily mean death, they could probably get fished out and rescued.
Long story short, hopping is likely the way to go, and perhaps, either some kind of snow-shoe feature or perhaps an ice/jagged edges feature if parts of Titan's surface are slippery. I'm far from an expert in such things, this is just my best guess.
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2019-02-21 03:36:39
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https://rspatial.github.io/raster/reference/spplot.html
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A wrapper function around spplot (sp package). With spplot it is easy to map several layers with a single legend for all maps. ssplot is itself a wrapper around the levelplot function in the lattice package, and see the help for these functions for additional options.
One of the advantages of the wrapper function for Raster* objects is the additional maxpixels argument to sample large objects for faster drawing.
There are also added spplot methods for Spatial objects that have no data.frame and for SpatVector (terra package)
# S4 method for Raster
spplot(obj, ..., maxpixels=50000, as.table=TRUE, zlim)
## Arguments
obj
Raster* object
...
Any argument that can be passed to spplot and levelplot
maxpixels
integer. Number of pixels to sample from each layer of large Raster objects
as.table
If TRUE, the plots are ordered from top to bottom
zlim
Vector of two elements indicating the minimum and maximum values to be mapped (values outside that ranage are set to these limits)
plot, plotRGB
The rasterVis package has more advanced plotting methods for Raster objects
## Examples
r <- raster(system.file("external/test.grd", package="raster"))
s <- stack(r, r*2)
names(s) <- c('meuse', 'meuse x 2')
spplot(s)
pts <- data.frame(sampleRandom(r, 10, xy=TRUE))
coordinates(pts) <- ~ x + y
spplot(s, scales = list(draw = TRUE),
xlab = "easting", ylab = "northing",
col.regions = rainbow(99, start=.1),
names.attr=c('original', 'times two'),
sp.layout = list("sp.points", pts, pch=20, cex=2, col='black'),
par.settings = list(fontsize = list(text = 12)), at = seq(0, 4000, 500))
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2023-03-25 06:54:57
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http://mathoverflow.net/questions/114887/if-np-exptime-does-every-dtm-have-a-succinct-execution-proof/114892
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# If NP=EXPTIME, does every DTM have a succinct “execution proof”?
Let HALTS-IN-N be the canonical $EXPTIME$-complete language {<$M$,$n$> | the deterministic Turing machine (DTM) encoded by $M$ halts in $n$ or fewer steps, with $n$ encoded in binary}. Since HALTS-IN-N is accepted in $EXPTIME$ by simulating $M$ for $n$ steps (or until it halts, whichever comes first), its complement is also $EXPTIME$-complete just by swapping the "accept" and "reject" states.
Define the execution trace of a DTM to be the string of transitions its finite control goes through in the process of accepting an input.
A language is in $NP$ if each string in the language has a polynomially-sized certificate with which that string's membership in the language can be verified in polynomial time.
Now suppose $NP=EXPTIME$. Then every instance of HALTS-IN-N has a certificate that $M$ halts in $n$ steps, and this certificate has size polynomial in the size of <$M$,$n$>, which has size logarithmic in the size of $M$'s execution trace (because $n$ is encoded in binary.)
Put another way, the fact that any DTM has halted or not after $n$ steps has two witnesses: its execution trace (size $n$) and its certificate (size logarithmic in $n$).
Question 1: Is the above reasoning valid?
I think the biggest candidate for a hole in it is that I'm assuming |$M$| is essentially a constant. For a particular $M$ it is, but I don't know if it poses problems when generalizing the statement to every DTM.
Question 2 (soft): If it is valid, how surprising are the consequences?
It sounded quite surprising to me initially, but then I started looking at execution traces of Busy Beaver TM's and realized that there is a lot of redundancy in them; it's not unimaginable to me that a DTM that halts in 47 million steps could have a proof of that fact that is much shorter.
But this part still does seem surprising: in this scenario, you could apparently "run" a DTM not by simulating it step-by-step, but rather by searching for this logarithmically-shorter execution proof.
In fact, what prevents me from finding an execution proof in exponential time even when $M$ represents some problem known to be outside $EXPTIME$? I can't see it yet, but there must be something; it's inconceivable that $NP$ and $EXPTIME$ could be separated with such a simple argument!
EDIT: As Emil Jeřábek pointed out, I meant polylogarithmic when I wrote logarithmic (apologies for the sloppiness.) Perhaps I should also have added "(relative to the surprisingness of other known consequences of NP=EXPTIME)" to question 2.
I'll try to give a concrete example for my last paragraph. Consider a DTM that initially writes an encoding of a primitive recursive function to its tape and which then proceeds to simulate that function, reading it off the tape -- call this machine $M$. An upper bound (not tight) on the maximum running time of the function should not be difficult to discover by examining its loops -- call this $n$. Have the DTM halt immediately if the function computes some value, but have it loop $n$ more times before halting if it computes some other value. (Or use some equivalent trick to tie the result of the function to the number of steps in which the DTM halts.)
The set of such DTMs is outside $PR$ (which is known to be outside $EXPTIME$), but still in $R$, as they always halt. But such <$M$,$n$> pairs could be given as instances of HALTS-IN-N, and (under the assumption $NP=EXPTIME$) proofs that they halt or not in $n$ steps could be found in time exponential in |<$M$,$n$>|.
Is it just that $n$ is necessarily so enormous that |<$M$,$n$>| is itself enormous, so that time exponential in it is in the territory of the Ackermann function?
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Q1: Yes (except that the certificates you get may have size polylogarithmic in $n$, not just logarithmic, and you need to apply the argument to both HALTS-IN-N and its complement, as pointed out by Andreas).
Q2: Well, NP = EXP contradicts all kinds of conjectures from complexity theory: it makes the polynomial hierarchy collapse to NP = coNP, it makes NP = PSPACE, and PSPACE = EXP, all of which are assumed to be false. On the other hand, it also implies P ≠ NP. We cannot rule out NP = EXP with the present state of knowledge (nor the even stronger collapse ZPP = EXP), but the time hierarchy theorem implies that $\mathrm P\ne\mathrm{EXP}$ and $\mathrm{NP}\ne\mathrm{NEXP}\cap\mathrm{coNEXP}$. Existence of succinct certificates also shows up in other similar situations: for example, if EXP has polynomial-size Boolean circuits, then membership in any EXP language has succinct certificates verifiable in randomized polynomial time (that is, EXP = MA).
Vis-à-vis the last but one paragraph of your question, note that an exhaustive deterministic search for a short certificate takes time exponential in the size of the certificate, so you don’t save here anything in terms of deterministic running time.
I don’t follow the last paragraph. EXP = NP implies $\mathrm{DTIME}(2^{t(n)})\subseteq\mathrm{NTIME}\bigl(t(n)^{O(1)}\bigr)$ for every time-constructible function $t(n)$ of at least polynomial growth, if that’s what you mean, but this does not lead to a contradiction.
EDIT: It may be worth mentioning that there is nothing particularly revolting about the idea that the existence of an exponentially long computation can be proved using a polynomial amount of data. In fact, Babai, Fortnow, and Lund have shown that NEXP = MIP, which means that two (computationally unlimited) agents presenting polynomial-size evidence who cannot communicate with each other can reliably convince a randomized polynomial-time verifier that such an exponentially long halting computation (even nondeterministic) exists. (Here, polynomial and exponential is measured in terms of the length of the input, which is logarithmic in the $n$ from the original question.)
EDIT 2: Yes, the running times for primitive recursive functions (or predicates) are enormous. More precisely, a function is primitive recursive if and only if it is computable in time $A(k,n)$ for some constant $k$, where $A$ is the Ackermann function. Plugging an extra exponential or logarithm in this characterization makes no difference. In view of the latter fact, whether NP = EXP or not has not much to do with the argument: we know unconditionally that the version of HALTS-IN-N where $n$ is given in unary is in P.
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I worry about the "or not" in the sentence immediately before Question 1. The execution trace tells us whether or not the computation halts, but the smaller certificate only tells us that it has halted. – Andreas Blass Nov 29 '12 at 17:55
Aha. You are right that this does not strictly follow from the reasoning presented in the question. However, if NP = EXP, then the complement of HALTS-IN-N is in NP as well, so you can certify that the computation does not halt in the same way. – Emil Jeřábek Nov 29 '12 at 18:14
Right, that's why I mentioned the complement in the first paragraph (although I failed to work it into the rest of the argument in a coherent way, sorry.) I guess you could also say this as "EXP=Co-EXP", but I don't think I've ever seen it put that way. I don't think it depends on NP=EXP, does it? – Chris Pressey Nov 29 '12 at 19:23
Yes, EXP = coEXP follows more or less immediately from the definition, which is the likely reason why the notation coNEXP is rarely seen in the first place. – Emil Jeřábek Nov 29 '12 at 19:41
Thank you. I doubt that these hypothetical polylogarithmic execution proofs could be useful for much, but as computational oddities, I find them pleasing, and it's nice to know I wasn't just deluding myself into this conclusion. (It's also sobering to be reminded how much I've forgotten about the primitive recursive functions!) – Chris Pressey Dec 2 '12 at 18:57
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2013-12-12 20:14:20
|
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https://projecteuclid.org/euclid.nmj/1367242338
|
## Nagoya Mathematical Journal
### Generic formal fibers and analytically ramified stable rings
Bruce Olberding
#### Abstract
Let $A$ be a local Noetherian domain of Krull dimension $d$. Heinzer, Rotthaus, and Sally have shown that if the generic formal fiber of $A$ has dimension $d-1$, then $A$ is birationally dominated by a 1-dimensional analytically ramified local Noetherian ring having residue field finite over the residue field of $A$. We explore further this correspondence between prime ideals in the generic formal fiber and 1-dimensional analytically ramified local rings. Our main focus is on the case where the analytically ramified local rings are stable, and we show that in this case the embedding dimension of the stable ring reflects the embedding dimension of a prime ideal maximal in the generic formal fiber, thus providing a measure of how far the generic formal fiber deviates from regularity. A number of characterizations of analytically ramified local stable domains are also given.
#### Article information
Source
Nagoya Math. J., Volume 211 (2013), 109-135.
Dates
First available in Project Euclid: 29 April 2013
Permanent link to this document
https://projecteuclid.org/euclid.nmj/1367242338
Digital Object Identifier
doi:10.1215/00277630-2148583
Mathematical Reviews number (MathSciNet)
MR3079281
Zentralblatt MATH identifier
1278.13020
#### Citation
Olberding, Bruce. Generic formal fibers and analytically ramified stable rings. Nagoya Math. J. 211 (2013), 109--135. doi:10.1215/00277630-2148583. https://projecteuclid.org/euclid.nmj/1367242338
#### References
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• [24] B. Olberding, “Stability of ideals and its applications” in Ideal Theoretic Methods in Commutative Algebra (Columbia, Mo., 1999), Lecture Notes Pure Appl. Math. 220, Dekker, New York, 2001, 319–341.
• [25] B. Olberding, On the structure of stable domains, Comm. Algebra 30 (2002), 877–895.
• [26] B. Olberding, A counterpart to Nagata idealization, J. Algebra 365 (2012), 199–221.
• [27] B. Olberding, One-dimensional bad Noetherian rings, to appear in Trans. Amer. Math. Soc., preprint, arXiv:1208.2913 [math.AC]
• [28] G. Picozza and F. Tartarone, Flat ideals and stability in integral domains, J. Algebra 324 (2010), 1790–1802.
• [29] J. D. Sally and W. V. Vasconcelos, Stable rings and a problem of Bass, Bull. Amer. Math. Soc. (N.S.) 79 (1973), 574–576.
• [30] J. Sally and W. Vasconcelos, Stable rings, J. Pure Appl. Algebra 4 (1974), 319–336.
• [31] F. K. Schmidt, Über die Erhaltung der Kettensätze der Idealtheorie bei beliebigen endlichen Körpererweiterungen, Math. Z. 41 (1936), 443–450.
• [32] L. Sega, Ideal class semigroups of overrings, J. Algebra 311 (2007), 702–713.
• [33] P. Zanardo, The class semigroup of local one-dimensional domains, J. Pure Appl. Algebra 212 (2008), 2259–2270.
• [34] P. Zanardo, Algebraic entropy of endomorphisms over local one-dimensional domains, J. Algebra Appl. 8 (2009), 759–777.
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2020-01-26 23:26:14
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https://math.stackexchange.com/questions/1944343/fast-eigenvector-calculation-of-markov-state-transition-probability
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# Fast Eigenvector calculation of Markov state transition probability
I have a problem in hand that involves calculation of eigenvector of a large sparse matrix ($10^7 \times 10^7$). A first-order Markov chain is fit to the problem, and the state transition probability matrix has only 7 non-zero entries at each column. I used power method and Rayleigh quotient method to quickly calculate the steady state occupancy distribution, and finally MATLAB's eigs function with the option to return only the largest eigen pair.
Apart from which method is more efficient and all that, even the construction of the state transition probability matrix takes some time. Numerical analysis is not my field, but I was wondering if the the following facts can help me to improve the calculation speed:
• I'm only interested in eigenvector corresponding to the largest eigenvalue (which is obviously 1)
• the non-zero entries of the matrix can be calculated on the fly, I mean there is routine $f$ which $p_{ij} = f(i, j)$, $\text{P}=[p_{ij}]$ is the state transition probability matrix.
Any help/reference is much appreciated.
• Do you have an idea of the order of magnitude of $1-\lambda_2$, where $\lambda_2$ is the second largest eigenvalue? Also, it may be possible to try to find the stationary distribution by actually solving the system $\pi P=P,\sum_i \pi_i=1$ using a sparse linear system routine instead of an eigenvalue routine. My concern with that is that you are solving $n+1$ equations in $n$ unknowns, which is a rank deficient problem, which can sometimes cause problems. The easy fixes (e.g. taking an SVD) destroy sparsity. Also, is your transition matrix symmetric or not? – Ian Sep 28 '16 at 0:43
• @ByronSchmuland, thanks. I fixed that. – Ali Sep 28 '16 at 0:45
• @Ian, no unfortunately I don't have any other side information, and the matrix is not symmetric. – Ali Sep 28 '16 at 0:46
• You can solve $n$ equations in $n$ unknowns: $\sum_i \pi_i = 1$ and $n-1$ of the $n$ entries of $\pi P = \pi$; since the row sums are all $1$, the omitted equation is a consequence of these. – Robert Israel Sep 28 '16 at 0:59
• @RobertIsrael, thanks for the comment. I actually tried this but didn't help me much as I have to construct P matrix again. As I mentioned this also takes quite some time, the routine $f$ in my post is not a simple on-line equation and has to be called $7 \times 10^7$ to construct the matrix :( – Ali Sep 28 '16 at 1:05
You need to have an efficient method for forming a sparse-dense multiplication $Av$ many times for different $v$. If the matrix $A$ does not have any special structure, that can speed up forming $Av$, then you need to costruct this matrix explicitly. Calculating elements of $A$ on the fly will only slow down computations considerably, since all elements of $A$ will be recalculated many times.
• As a remark, eigs can take a function handle representation of the matrix rather than the matrix itself. This might be faster than actually assembling A, though I'm a bit skeptical of that; if we naively assume that storing $7 \times 10^7$ entries of a sparse matrix takes $21 \times 10^7$ doubles, then that's about $1.7 \times 10^9$ bytes, which is large but fits in RAM. And I think the actual sparse matrix implementation is a bit more clever than that. By comparison, dynamically recomputing those entries using a function handle might very well be quite a bit slower. – Ian Sep 28 '16 at 2:23
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2019-12-09 22:43:04
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http://image.absoluteastronomy.com/topics/Cartesian_closed_category
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Cartesian closed category
Encyclopedia
In category theory
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
, a category is cartesian closed if, roughly speaking, any morphism
Morphism
In mathematics, a morphism is an abstraction derived from structure-preserving mappings between two mathematical structures. The notion of morphism recurs in much of contemporary mathematics...
defined on a product
Product (category theory)
In category theory, the product of two objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the cartesian product of sets, the direct product of groups, the direct product of rings and the product of topological spaces...
of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
and the theory of programming, in that they provide a natural setting for lambda calculus
Lambda calculus
In mathematical logic and computer science, lambda calculus, also written as λ-calculus, is a formal system for function definition, function application and recursion. The portion of lambda calculus relevant to computation is now called the untyped lambda calculus...
. For generalizations of this notion to monoidal categories
Monoidal category
In mathematics, a monoidal category is a category C equipped with a bifunctorwhich is associative, up to a natural isomorphism, and an object I which is both a left and right identity for ⊗, again up to a natural isomorphism...
, see closed monoidal category
Closed monoidal category
In mathematics, especially in category theory, aclosed monoidal category is a context where we can take tensor products of objects and also form 'mapping objects'. A classic example is the category of sets, Set, where the tensor product of sets A and B is the usual cartesian product A \times B, and...
.
## Definition
The category C is called Cartesian closed if and only if
If and only if
In logic and related fields such as mathematics and philosophy, if and only if is a biconditional logical connective between statements....
it satisfies the following three properties:
• It has a terminal object.
• Any two objects X and Y of C have a product
Product (category theory)
In category theory, the product of two objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the cartesian product of sets, the direct product of groups, the direct product of rings and the product of topological spaces...
X×Y in C.
• Any two objects Y and Z of C have an exponential
Exponential object
In mathematics, specifically in category theory, an exponential object is the categorical equivalent of a function space in set theory. Categories with all finite products and exponential objects are called cartesian closed categories...
ZY in C.
The first two conditions can be combined to the single requirement that any finite (possibly empty) family of objects of C admit a product
Product (category theory)
In category theory, the product of two objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the cartesian product of sets, the direct product of groups, the direct product of rings and the product of topological spaces...
in C, because of the natural associativity
Associativity
In mathematics, associativity is a property of some binary operations. It means that, within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not...
of the categorical product and because the empty product
Empty product
In mathematics, an empty product, or nullary product, is the result of multiplying no factors. It is equal to the multiplicative identity 1, given that it exists for the multiplication operation in question, just as the empty sum—the result of adding no numbers—is zero, or the additive...
in a category is the terminal object of that category.
The third condition is equivalent to the requirement that the functor
Functor
In category theory, a branch of mathematics, a functor is a special type of mapping between categories. Functors can be thought of as homomorphisms between categories, or morphisms when in the category of small categories....
–×Y (i.e. the functor from C to C that maps objects X to X×Y and morphisms φ to φ×idY) has a right adjoint
In mathematics, adjoint functors are pairs of functors which stand in a particular relationship with one another, called an adjunction. The relationship of adjunction is ubiquitous in mathematics, as it rigorously reflects the intuitive notions of optimization and efficiency...
, usually denoted –Y, for all objects Y in C.
For locally small categories, this can be expressed by the existence of a bijection
Bijection
A bijection is a function giving an exact pairing of the elements of two sets. A bijection from the set X to the set Y has an inverse function from Y to X. If X and Y are finite sets, then the existence of a bijection means they have the same number of elements...
between the hom-sets
which is natural
Natural transformation
In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure of the categories involved. Hence, a natural transformation can be considered to be a "morphism of functors". Indeed this intuition...
in both X and Z.
If a category is such that all its slice categories are cartesian closed, then it is called locally cartesian closed.
## Examples
Examples of cartesian closed categories include:
• The category Set of all sets, with function
Function (mathematics)
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
s as morphisms, is cartesian closed. The product X×Y is the cartesian product of X and Y, and ZY is the set of all functions from Y to Z. The adjointness is expressed by the following fact: the function f : X×YZ is naturally identified with the curried
Currying
In mathematics and computer science, currying is the technique of transforming a function that takes multiple arguments in such a way that it can be called as a chain of functions each with a single argument...
function g : XZY defined by g(x)(y) = f(x,y) for all x in X and y in Y.
• The category of finite sets, with functions as morphisms, is cartesian closed for the same reason.
• If G is a group
Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity...
, then the category of all G-sets
Group action
In algebra and geometry, a group action is a way of describing symmetries of objects using groups. The essential elements of the object are described by a set, and the symmetries of the object are described by the symmetry group of this set, which consists of bijective transformations of the set...
is cartesian closed. If Y and Z are two G-sets, then ZY is the set of all functions from Y to Z with G action defined by (g.F)(y) = g.(F(g-1.y)) for all g in G, F:YZ and y in Y.
• The category of finite G-sets is also cartesian closed.
• The category Cat of all small categories (with functors as morphisms) is cartesian closed; the exponential CD is given by the functor category
Functor category
In category theory, a branch of mathematics, the functors between two given categories form a category, where the objects are the functors and the morphisms are natural transformations between the functors...
consisting of all functors from D to C, with natural transformation
Natural transformation
In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure of the categories involved. Hence, a natural transformation can be considered to be a "morphism of functors". Indeed this intuition...
s as morphisms.
• If C is a small category, then the functor category
Functor category
In category theory, a branch of mathematics, the functors between two given categories form a category, where the objects are the functors and the morphisms are natural transformations between the functors...
SetC consisting of all covariant functors from C into the category of sets, with natural transformation
Natural transformation
In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure of the categories involved. Hence, a natural transformation can be considered to be a "morphism of functors". Indeed this intuition...
s as morphisms, is cartesian closed. If F and G are two functors from C to Set, then the exponential FG is the functor whose value on the object X of C is given by the set of all natural transformations from (X,−) × G to F.
• The earlier example of G-sets can be seen as a special case of functor categories: every group can be considered as a one-object category, and G-sets are nothing but functors from this category to Set
• The category of all directed graphs
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
is cartesian closed; this is a functor category as explained under functor category
Functor category
In category theory, a branch of mathematics, the functors between two given categories form a category, where the objects are the functors and the morphisms are natural transformations between the functors...
.
• In algebraic topology
Algebraic topology
Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.Although algebraic topology...
, cartesian closed categories are particularly easy to work with. Neither the category of topological space
Topological space
Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion...
s with continuous maps nor the category of smooth manifolds
Manifold
In mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....
with smooth maps is cartesian closed. Substitute categories have therefore been considered: the category of compactly generated Hausdorff spaces is cartesian closed, as is the category of Frölicher space
Frölicher space
In mathematics, Frölicher spaces extend the notions of calculus and smooth manifolds. They were introduced in 1982 by the mathematician Alfred Frölicher.-Definition:...
s.
• In order theory
Order theory
Order theory is a branch of mathematics which investigates our intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article introduces the field and gives some basic definitions...
, complete partial order
Complete partial order
In mathematics, directed complete partial orders and ω-complete partial orders are special classes of partially ordered sets, characterized by particular completeness properties...
s (cpos) have a natural topology, the Scott topology, whose continuous maps do form a cartesian closed category (that is, the objects are the cpos, and the morphisms are the Scott continuous maps). Both currying
Currying
In mathematics and computer science, currying is the technique of transforming a function that takes multiple arguments in such a way that it can be called as a chain of functions each with a single argument...
and apply
Apply
In mathematics and computer science, Apply is a function that applies functions to arguments. It is central to programming languages derived from lambda calculus, such as LISP and Scheme, and also in functional languages...
are continuous functions in the Scott topology, and currying, together with apply, provide the adjoint.
• A Heyting algebra
Heyting algebra
In mathematics, a Heyting algebra, named after Arend Heyting, is a bounded lattice equipped with a binary operation a→b of implication such that ∧a ≤ b, and moreover a→b is the greatest such in the sense that if c∧a ≤ b then c ≤ a→b...
is a Cartesian closed (bounded) lattice
Lattice (order)
In mathematics, a lattice is a partially ordered set in which any two elements have a unique supremum and an infimum . Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities...
. An important example arises from topological space
Topological space
Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion...
s. If X is a topological space
Topological space
Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion...
, then the open set
Open set
The concept of an open set is fundamental to many areas of mathematics, especially point-set topology and metric topology. Intuitively speaking, a set U is open if any point x in U can be "moved" a small amount in any direction and still be in the set U...
s in X form the objects of a category O(X) for which there is a unique morphism from U to V if U is a subset of V and no morphism otherwise. This poset is a cartesian closed category: the "product" of U and V is the intersection of U and V and the exponential UV is the interior
Interior (topology)
In mathematics, specifically in topology, the interior of a set S of points of a topological space consists of all points of S that do not belong to the boundary of S. A point that is in the interior of S is an interior point of S....
of U∪(X\V).
The following categories are not cartesian closed:
• The category of all vector space
Vector space
A vector space is a mathematical structure formed by a collection of vectors: objects that may be added together and multiplied by numbers, called scalars in this context. Scalars are often taken to be real numbers, but one may also consider vector spaces with scalar multiplication by complex...
s over some fixed field
Field (mathematics)
In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it is an algebraic structure with notions of addition, subtraction, multiplication, and division, satisfying certain axioms...
is not cartesian closed; neither is the category of all finite-dimensional vector spaces. While they have products (called direct sums), the product functors do not have right adjoints. (They are, however, symmetric monoidal closed categories: the set of linear transformations between two vector spaces forms another vector space, so they are closed, and if one replaces the product by the tensor product
Tensor product
In mathematics, the tensor product, denoted by ⊗, may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, and modules, among many other structures or objects. In each case the significance of the symbol is the same: the most general...
, a similar isomorphism exists between the Hom spaces.)
• The category of abelian group
Abelian group
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on their order . Abelian groups generalize the arithmetic of addition of integers...
s is not cartesian closed, for the same reason.
## Applications
In cartesian closed categories, a "function of two variables" (a morphism f:X×YZ) can always be represented as a "function of one variable" (the morphism λf:XZY). In computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
applications, this is known as currying
Currying
In mathematics and computer science, currying is the technique of transforming a function that takes multiple arguments in such a way that it can be called as a chain of functions each with a single argument...
; it has led to the realization that simply-typed lambda calculus can be interpreted in any cartesian closed category.
The Curry-Howard-Lambek correspondence provides a deep isomorphism between intuitionistic logic, simply-typed lambda calculus and cartesian closed categories.
Certain cartesian closed categories, the topoi
Topos
In mathematics, a topos is a type of category that behaves like the category of sheaves of sets on a topological space...
, have been proposed as a general setting for mathematics, instead of traditional set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
.
The renowned computer scientist John Backus
John Backus
John Warner Backus was an American computer scientist. He directed the team that invented the first widely used high-level programming language and was the inventor of the Backus-Naur form , the almost universally used notation to define formal language syntax.He also did research in...
has advocated a variable-free notation, or Function-level programming
Function-level programming
In computer science, function-level programming refers to one of the two contrasting programming paradigms identified by John Backus in his work on programs as mathematical objects, the other being value-level programming....
, which in retrospect bears some similarity to the internal language of cartesian closed categories. CAML is more consciously modelled on cartesian closed categories.
## Equational theory
In every cartesian closed category (using exponential notation), (XY)Z and (XZ)Y are isomorphic for all objects X, Y and Z. We write this as the "equation"
z = (xz)y.
One may ask what other such equations are valid in all cartesian closed categories. It turns out that all of them follow logically from the following axioms:
• x×(y×z) = (x×yz
• x×y = y×x
• x×1 = x (here 1 denotes the terminal object of C)
• 1x = 1
• x1 = x
• (x×y)z = xz×yz
• (xy)z = x(y×z)
Bicartesian closed categories extend cartesian closed categories with binary coproduct
Coproduct
In category theory, the coproduct, or categorical sum, is the category-theoretic construction which includes the disjoint union of sets and of topological spaces, the free product of groups, and the direct sum of modules and vector spaces. The coproduct of a family of objects is essentially the...
s and an initial object
Initial object
In category theory, an abstract branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely one morphism I → X...
, with products distributing over coproducts. Their equational theory is extended with the following axioms:
• x + y = y + x
• (x + y) + z = x + (y + z)
• x(y + z) = xy + xz
• x(y + z) = xyxz
• 0 + x = x
• x×0 = 0
• x0 = 1
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2023-03-23 01:31:08
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http://www.nag.com/numeric/fl/nagdoc_fl24/html/G02/g02hbf.html
|
G02 Chapter Contents
G02 Chapter Introduction
NAG Library Manual
# NAG Library Routine DocumentG02HBF
Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.
## 1 Purpose
G02HBF finds, for a real matrix $X$ of full column rank, a lower triangular matrix $A$ such that ${\left({A}^{\mathrm{T}}A\right)}^{-1}$ is proportional to a robust estimate of the covariance of the variables. G02HBF is intended for the calculation of weights of bounded influence regression using G02HDF.
## 2 Specification
SUBROUTINE G02HBF ( UCV, N, M, X, LDX, A, Z, BL, BD, TOL, MAXIT, NITMON, NIT, WK, IFAIL)
INTEGER N, M, LDX, MAXIT, NITMON, NIT, IFAIL REAL (KIND=nag_wp) UCV, X(LDX,M), A(M*(M+1)/2), Z(N), BL, BD, TOL, WK(M*(M+1)/2) EXTERNAL UCV
## 3 Description
In fitting the linear regression model
$y=Xθ+ε,$
where $y$ is a vector of length $n$ of the dependent variable, $X$ is an $n$ by $m$ matrix of independent variables, $\theta$ is a vector of length $m$ of unknown parameters, and $\epsilon$ is a vector of length $n$ of unknown errors,
it may be desirable to bound the influence of rows of the $X$ matrix. This can be achieved by calculating a weight for each observation. Several schemes for calculating weights have been proposed (see Hampel et al. (1986) and Marazzi (1987)). As the different independent variables may be measured on different scales one group of proposed weights aims to bound a standardized measure of influence. To obtain such weights the matrix $A$ has to be found such that
$1n∑i=1nuzi2zi ziT =I I is the identity matrix$
and
$zi=Axi,$
where ${x}_{i}$ is a vector of length $m$ containing the elements of the $i$th row of $X$, $A$ is an $m$ by $m$ lower triangular matrix, ${z}_{i}$ is a vector of length $m$, and $u$ is a suitable function.
The weights for use with G02HDF may then be computed using
$wi=fzi2$
for a suitable user-supplied function $f$.
G02HBF finds $A$ using the iterative procedure
$Ak=Sk+IAk-1,$
where ${S}_{k}=\left({s}_{jl}\right)$, for $\mathit{j}=1,2,\dots ,m$ and $\mathit{l}=1,2,\dots ,m$, is a lower triangular matrix such that
• ${s}_{jl}=\left\{\begin{array}{ll}-\mathrm{min}\phantom{\rule{0.125em}{0ex}}\left[\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left({h}_{jl}/n,-\mathit{BL}\right),\mathit{BL}\right]\text{,}& j>l\\ & \\ -\mathrm{min}\phantom{\rule{0.125em}{0ex}}\left[\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(\frac{1}{2}\left({h}_{jj}/n-1\right),-\mathit{BD}\right),\mathit{BD}\right]\text{,}& j=l\end{array}\right\$
• ${h}_{jl}=\sum _{i=1}^{n}u\left({‖{z}_{i}‖}_{2}\right){z}_{ij}{z}_{il}$
and $\mathit{BD}$ and $\mathit{BL}$ are suitable bounds.
In addition the values of ${‖{z}_{i}‖}_{2}$, for $i=1,2,\dots ,n$, are calculated.
G02HBF is based on routines in ROBETH; see Marazzi (1987).
## 4 References
Hampel F R, Ronchetti E M, Rousseeuw P J and Stahel W A (1986) Robust Statistics. The Approach Based on Influence Functions Wiley
Huber P J (1981) Robust Statistics Wiley
Marazzi A (1987) Weights for bounded influence regression in ROBETH Cah. Rech. Doc. IUMSP, No. 3 ROB 3 Institut Universitaire de Médecine Sociale et Préventive, Lausanne
## 5 Parameters
1: UCV – REAL (KIND=nag_wp) FUNCTION, supplied by the user.External Procedure
UCV must return the value of the function $u$ for a given value of its argument. The value of $u$ must be non-negative.
The specification of UCV is:
FUNCTION UCV ( T)
REAL (KIND=nag_wp) UCV
REAL (KIND=nag_wp) T
1: T – REAL (KIND=nag_wp)Input
On entry: the argument for which UCV must be evaluated.
UCV must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which G02HBF is called. Parameters denoted as Input must not be changed by this procedure.
2: N – INTEGERInput
On entry: $n$, the number of observations.
Constraint: ${\mathbf{N}}>1$.
3: M – INTEGERInput
On entry: $m$, the number of independent variables.
Constraint: $1\le {\mathbf{M}}\le {\mathbf{N}}$.
4: X(LDX,M) – REAL (KIND=nag_wp) arrayInput
On entry: the real matrix $X$, i.e., the independent variables. ${\mathbf{X}}\left(\mathit{i},\mathit{j}\right)$ must contain the $\mathit{i}\mathit{j}$th element of ${\mathbf{X}}$, for $\mathit{i}=1,2,\dots ,n$ and $\mathit{j}=1,2,\dots ,m$.
5: LDX – INTEGERInput
On entry: the first dimension of the array X as declared in the (sub)program from which G02HBF is called.
Constraint: ${\mathbf{LDX}}\ge {\mathbf{N}}$.
6: A(${\mathbf{M}}×\left({\mathbf{M}}+1\right)/2$) – REAL (KIND=nag_wp) arrayInput/Output
On entry: an initial estimate of the lower triangular real matrix $A$. Only the lower triangular elements must be given and these should be stored row-wise in the array.
The diagonal elements must be $\text{}\ne 0$, although in practice will usually be $\text{}>0$. If the magnitudes of the columns of $X$ are of the same order the identity matrix will often provide a suitable initial value for $A$. If the columns of $X$ are of different magnitudes, the diagonal elements of the initial value of $A$ should be approximately inversely proportional to the magnitude of the columns of $X$.
On exit: the lower triangular elements of the matrix $A$, stored row-wise.
7: Z(N) – REAL (KIND=nag_wp) arrayOutput
On exit: the value ${‖{z}_{\mathit{i}}‖}_{2}$, for $\mathit{i}=1,2,\dots ,n$.
8: BL – REAL (KIND=nag_wp)Input
On entry: the magnitude of the bound for the off-diagonal elements of ${S}_{k}$.
Suggested value: ${\mathbf{BL}}=0.9$.
Constraint: ${\mathbf{BL}}>0.0$.
9: BD – REAL (KIND=nag_wp)Input
On entry: the magnitude of the bound for the diagonal elements of ${S}_{k}$.
Suggested value: ${\mathbf{BD}}=0.9$.
Constraint: ${\mathbf{BD}}>0.0$.
10: TOL – REAL (KIND=nag_wp)Input
On entry: the relative precision for the final value of $A$. Iteration will stop when the maximum value of $\left|{s}_{jl}\right|$ is less than TOL.
Constraint: ${\mathbf{TOL}}>0.0$.
11: MAXIT – INTEGERInput
On entry: the maximum number of iterations that will be used during the calculation of $A$.
A value of ${\mathbf{MAXIT}}=50$ will often be adequate.
Constraint: ${\mathbf{MAXIT}}>0$.
12: NITMON – INTEGERInput
On entry: determines the amount of information that is printed on each iteration.
${\mathbf{NITMON}}>0$
The value of $A$ and the maximum value of $\left|{s}_{jl}\right|$ will be printed at the first and every NITMON iterations.
${\mathbf{NITMON}}\le 0$
No iteration monitoring is printed.
When printing occurs the output is directed to the current advisory message unit (see X04ABF).
13: NIT – INTEGEROutput
On exit: the number of iterations performed.
14: WK(${\mathbf{M}}×\left({\mathbf{M}}+1\right)/2$) – REAL (KIND=nag_wp) arrayWorkspace
15: IFAIL – INTEGERInput/Output
On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.
On exit: ${\mathbf{IFAIL}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).
## 6 Error Indicators and Warnings
If on entry ${\mathbf{IFAIL}}={\mathbf{0}}$ or $-{\mathbf{1}}$, explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
${\mathbf{IFAIL}}=1$
On entry, ${\mathbf{N}}\le 1$, or ${\mathbf{M}}<1$, or ${\mathbf{N}}<{\mathbf{M}}$, or ${\mathbf{LDX}}<{\mathbf{N}}$.
${\mathbf{IFAIL}}=2$
On entry, ${\mathbf{TOL}}\le 0.0$, or ${\mathbf{MAXIT}}\le 0$, or diagonal element of ${\mathbf{A}}=0.0$, or ${\mathbf{BL}}\le 0.0$, or ${\mathbf{BD}}\le 0.0$.
${\mathbf{IFAIL}}=3$
Value returned by ${\mathbf{UCV}}<0$.
${\mathbf{IFAIL}}=4$
The routine has failed to converge in MAXIT iterations.
## 7 Accuracy
On successful exit the accuracy of the results is related to the value of TOL; see Section 5.
The existence of $A$ will depend upon the function $u$; (see Hampel et al. (1986) and Marazzi (1987)), also if $X$ is not of full rank a value of $A$ will not be found. If the columns of $X$ are almost linearly related then convergence will be slow.
## 9 Example
This example reads in a matrix of real numbers and computes the Krasker–Welsch weights (see Marazzi (1987)). The matrix $A$ and the weights are then printed.
### 9.1 Program Text
Program Text (g02hbfe.f90)
### 9.2 Program Data
Program Data (g02hbfe.d)
### 9.3 Program Results
Program Results (g02hbfe.r)
|
2016-02-11 07:19:14
|
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https://www.gradesaver.com/textbooks/math/calculus/thomas-calculus-13th-edition
|
## Thomas' Calculus 13th Edition
domain $(-\infty,\infty)$; range = $[1,\infty)$
Domain: $1+x^{2}$ is defined for all real numbers, so the domain is $(-\infty,\infty)$. Range: $x^{2}$ is always greater than or equal to 0, so $x^{2}+1\geq1$. This makes the range $[1,\infty)$
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2018-12-13 19:46:54
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http://www.theinfolist.com/html/ALL/s/diameter.html
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TheInfoList
In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for the diameter of a sphere. In more modern usage, the length of a diameter is also called the diameter. In this sense one speaks of ''the'' diameter rather than ''a'' diameter (which refers to the line segment itself), because all diameters of a circle or sphere have the same length, this being twice the radius r. : $d = 2r \quad \Rightarrow \quad r = \frac.$ For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the ''width'' is often defined to be the smallest such distance. Both quantities can be calculated efficiently using rotating calipers. For a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance. For an ellipse, the standard terminology is different. A diameter of an ellipse is any chord passing through the centre of the ellipse. For example, conjugate diameters have the property that a tangent line to the ellipse at the endpoint of one diameter is parallel to the conjugate diameter. The longest diameter is called the major axis. The word "diameter" is derived from grc|διάμετρος (), "diameter of a circle", from (), "across, through" and (), "measure". It is often abbreviated ''DIA'', ''dia'', ''d'', or ''⌀''.
Generalizations
The definitions given above are only valid for circles, spheres and convex shapes. However, they are special cases of a more general definition that is valid for any kind of ''n''-dimensional convex or non-convex object, such as a hypercube or a set of scattered points. The diameter of a subset of a metric space is the least upper bound of the set of all distances between pairs of points in the subset. So, if is the subset, the diameter is :sup . If the distance function is viewed here as having codomain R (the set of all real numbers), this implies that the diameter of the empty set (the case ) equals −∞ (negative infinity). Some authors prefer to treat the empty set as a special case, assigning it a diameter of 0, which corresponds to taking the codomain of to be the set of nonnegative reals. For any solid object or set of scattered points in ''n''-dimensional Euclidean space, the diameter of the object or set is the same as the diameter of its convex hull. In medical parlance concerning a lesion or in geology concerning a rock, the diameter of an object is the supremum of the set of all distances between pairs of points in the object. In differential geometry, the diameter is an important global Riemannian invariant. In plane geometry, a diameter of a conic section is typically defined as any chord which passes through the conic's centre; such diameters are not necessarily of uniform length, except in the case of the circle, which has eccentricity ''e'' = 0.
Symbol
150px|Sign from an shx_font_with_an_angle_16°._This_font_does_not_contain_..html" style="text-decoration: none;"class="mw-redirect" title="shapefile.html" style="text-decoration: none;"class="mw-redirect" title="AutoCAD drawing in dim.[[shapefile">shx font with an angle 16°. This font does not contain .">shapefile.html" style="text-decoration: none;"class="mw-redirect" title="AutoCAD drawing in dim.[[shapefile">shx font with an angle 16°. This font does not contain . The [[symbol or [[variable (mathematics)|variable for diameter, , is sometimes used in technical drawings or specifications as a prefix or suffix for a number (e.g. "⌀ 55 mm", indicating that it represents diameter. For example, photographic filter thread sizes are often denoted in this way. In German, the diameter symbol (German ''Durchmesserzeichen'') is also used as an average symbol (''Durchschnittszeichen'').
Similar symbols
It is similar in size and design to , the Latin small letter o with stroke. The diameter symbol ⌀ is distinct from the empty set symbol , from an (italic) uppercase phi , and from the Nordic vowel (Latin capital letter O with stroke). See also slashed zero.
Encodings
The symbol has a Unicode code point at , in the Miscellaneous Technical set. On an Apple Macintosh, the diameter symbol can be entered via the character palette (this is opened by pressing in most applications), where it can be found in the Technical Symbols category. In Unix/Linux/ChromeOS systems, it is generated using It can be obtained in UNIX-like operating systems using a Compose key by pressing, in sequence, The character will sometimes not display correctly, however, since many fonts do not include it. In many situations the letter ø (the Latin small letter o with stroke) is an acceptable substitute, which in Unicode is . and on a Macintosh by pressing (the letter o, not the number 0). In Unix/Linux/ChromeOS systems, it is generated using or . AutoCAD uses available as a shortcut string . In Microsoft Word the diameter symbol can be acquired by typing 2300 and then pressing Alt+X. In LaTeX the diameter symbol can be obtained with the command \diameter from the wasysym package.
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2021-09-26 13:34:58
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http://mlwiki.org/index.php?title=K-Means_LSH&oldid=766&diff=prev&printable=yes
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# ML Wiki
## K-Means LSH
Many of LSH families are structured quantizers: they don't take into account underlying statistics
• for example, E2LSH is structured:
• we choose only quantization step $w$ and offset $b$ and have little influence on the density of individual cells
• but can address this issue by learning a Vector Quantizer - such as K-Means: this way we can adapt the cell size to the density of the space in the cell
### Learning Density with K-Means
Unstructured VQ:
• let $\mathcal R \to [ \, 1, 2, \ ... \ , k \, ]$
• and $\mathbf x \to g(\mathbf x) = \mathop{arg min}\limits_{i = 1..k} L_2(\mathbf x, \boldsymbol \mu_i)$
• it maps each vector to a cell indexed by $g(\mathbf x)$
• $k$ is # of possible values of $g(\cdot)$
• $\boldsymbol \mu_i$ are centroids - they define the quantizer
• often learned with K-Means
Illustration:
• Euclidean LSH (Random Projection LSH) vs K-Means
• K-Means adapts to data while others don't
• source: Paulevé2010 figure 3
## KLSH: K-Means LSH
### Preprocessing
How to use K-Means to build a LSH?
• generate $L$ different clusterings on the same data by using different seeds
• after this we have $L$ codebooks (sets of centroids) $\{\mathbf c_{j1}, \ ... \ , \mathbf c_{jk}\}$, where $\mathbf c_{ji}$ is $i$th centroid of $j$'s clustering
• each centroid is an $h$ and codebooks is an $g$ in LSH
Indexing:
• a vector to index is assigned to the closest centroid found in a codebook
• use $L$ codebooks to have $L$ cluster assignments
### Querying
Search time:
• first nearest centroid for each codebook
• then keep only vectors that are assignment to the same centroids
query($\mathbf q$)
• $\text{res} = \varnothing$
• for $j = 1$ to $L$ do
• $i^* = \operatorname{arg\, mix}\limits_{i = 1 .. k} \| \mathbf q, \mathbf c_{ji} \|$
• $\text{res} = \text{res} \cup \big\{ \text{cluster}(\mathbf c_{ji^*}) \big\}$
• return $\text{res}$
## Improvements
### Multi-Probing
Multi-Probing for K-Means LSH:
• fix $m_p$ the number of buckets we want to retrieve
• for each $L$ hash functions
• select $m_p$ closets centroids
• then return all vectors from these $m_p$ centroids
Idea:
• a variation of Query-Adaptive LSH for K-Means LSH
• instead of a single k-means per hash maintain a pool of independent clustering results
• at the query time select the best one from the pool
• define a pool of $L$ hash functions (with $L$ larger than in usual LSHs)
• compute relevance criteria $\lambda_j$ for each $g_j$: this criteria identifies the hash functions that are more likely to return the NNs
• relevance could be: distance between the query and the center of the cell
• $\lambda_j(\mathbf q) = \min_{i = 1..k} \| \mathbf q, \mathbf c_{ji} \|$
• and $\lambda_j(\mathbf q)$ is actually a by-product of finding the nearest centroid
• so rank $g_j(\mathbf q)$ by $\lambda_j(\mathbf q)$ then pick $p$ best and use them
Notes:
• for this to be useful need $L$ larger than usual
• it gives better performance, but it becomes more computationally expensive - may be not very critical as it's done offline
## Sources
• Paulevé, Loïc, et al. "Locality sensitive hashing: A comparison of hash function types and querying mechanisms." 2010. [1]
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2021-12-04 23:14:34
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https://lizinan.wordpress.com/category/dissertation/
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## New Year Resolution
There are only a few hours in year 2010. Before the new year begins, I am going to make new year’s resolutions here.
1. Finishing my PhD study.
2. Finding a job.
3. Publishing at least one paper of my work.
4. Practicing writing skills through blogging every week.
If we are talking about superabsorbent polymer (SAP), we could not ignore the most famous book Modern Superabsorbent Polymer Technology edited by Fredreic L. Buchholz, and Andrew T. Graham from Dow Chemical. It gives a comprehensive review on the structure, properties, and applications of SAPs. In this book, the properties of SAPs varies with the synthesis chemistry has been discussed. Also, the comparison of industrial practices between major manufactures has been done. The analytical methods to evaluate the properties and behaviors of SAPs also were described within the context. New SAP products were introduced, too. Besides, the current and emerging applications of SAPs in personal care, horticulture, construction, and other areas have been mentioned. What a pity three is nothing about the applications of SAPs in oil and gas industry, what I have been done for a couple of years. Maybe because the book was born too early to cover this new application.
There are another two books in which an individual chapter reviewed the SAPs: Encyclopedia of Polymer Science and Technology(Vol. 8), and Ullmann’s Encyclopedia of Industrial Chemistry. Since both of the two sources only have around 20 pages, I prefer to the latter one, because which provided more well organized words.
## LaTeX Tricks (2)
I have been working on my dissertation using LaTeX for one week. Most of the contents came from my proposal. Now the structure has been set up and it is around 40 pages already. The next step is to fill the blanks. During the time period, I solved some problems by some tricks found on the Internet.
1. Upper or Lower case:
It is very easy to write upper or lower case in LaTeX. The cubic meter could be written as $m^3$ by $m^3$, but the display is mathematical, and the letters shows italics. If add \text in front of the code as $\text m^3$, the normal font appeared[1].
2. Multi-row Table:
Sometimes we need special tables. Multirow (multicolumn) command provide more choices.
Here is one simple example:
\begin{table}[h]
\centering \caption[Particle Size Distribution of
$\text{LiquiBlock}^{\texttrademark}$ 40K]{Particle Size Distribution
of $\text{LiquiBlock}^{\texttrademark}$ 40K}
\begin{tabular}{|r|r|r|r|}
\hline
\multirow{2}*{Mesh} & Size & Weight& Percentage \\
& (mm) & (g)& (\%) \\
\hline
18 & 1.000 & 9.14 & 2.29 \\
20 & 0.850 & 134.95 & 33.85 \\
30 & 0.600 & 134.21 & 33.66 \\
40 & 0.425 & 63.25 & 15.86 \\
45 & 0.355 & 20.85 & 5.23 \\
50 & 0.300 & 16.91 & 4.24 \\
60 & 0.250 & 14.90 & 3.74 \\
70 & 0.212 & 0.14 & 0.04 \\
$<$70 & $<$0.212 & 4.34 & 1.09 \\
\hline
\end{tabular}
\end{table}
It seems that wordpress does not support Table function of LaTeX. Please see the snapshot of the table below.
3. No Indent
Sometimes the journal requires no indent at the beginning of each paragraph[2].
\setlength{\parindent}{0pt}
Reference:
## LaTeX Tricks (1)
Last night a simple version of my dissertation has been created by LaTeX. As a fresh hand in LaTeX, there are so many things to learn, especially the tricks. A short summary for my work last night could be found below:
• Convert the .jpg file to .eps file:
LaTeX supports .eps files very well. It is possible to insert jpg pictures into LaTeX, also. From my experience last night, .jpg files maybe troublesome for LaTeX. Image-Pro Plus has ever been used to convert .jpg files into .eps files. Also, HP LaserJet 6P/6MP PostScript printer could do this job. Finally, I found another easy way. Now most TeX software embedded such kind of tools as bmeps.exe.[1] Type the following command under DOS mode in the folder where .jpg files are saved:
X:\bmeps *.jpg *.eps -c(if no -c, black and white pictures were generated).
• Insert .eps files in LaTeX
As previous description, LaTeX supported .eps files for a long time, and they linked with each other very well. All the textbooks about LaTeX just gave a brief instruction on how to insert .eps files in LaTeX. But, when I was trying to do the same thing following the instruction, the results disappointed me. After having done research on the Internet, I found latexpdf command could not read .eps files.[2] The solution is to compile the TEX files using latex command, then convert. dvi files into pdf using dvipdf command.
And another webpage I found last night provides more LaTeX tricks, which is kept here for future use.[3]
References:
## Converters from LaTeX to PC Textprocessors – Overview (by Wilfried Hennings)
Note: I determined to learn LaTeX around 5 years ago. At that time, a friend of mine gave me a book about how to use LaTeX. I also found some resources on the Internet. But due to limited use for my research and work, I do not have a chance to focus on it. LaTeX has so many advantages over other word processors like Microsoft Word. The relationship between LaTeX and Word is similar to that between keyboard and mouse. Mouse makes the operation easier, but keyboard is much more important and necessary. For common users, Word could satisfy their needs, but the equations and batch operations need LaTeX. In previous pages here, I insert some equations with LaTeX codes supported by WordPress. Because people around me do not use LaTeX very often, I had to find a way to convert my LaTeX files into Microsoft Word to exchange my ideas about research and work. Google found the useful information for me. In this blog, I forwarded an overview on converters between LaTeX and PC word processors for your and my own references.
Converters from LaTeX to PC Textprocessors – Overview
Switch conversion direction: From PC to LaTeX
Author: Wilfried Hennings (texconvfaq “at” gmx.de), this page last updated on Oct. 6, 2009
I maintain these pages because I need converters between LaTeX and PC Textprocessors for my work and I want to share the information with others who need it. Because I maintain them in my spare time (uh, what is spare time?), I can not answer individual questions.
This list is as good or as bad as its support, and it needs YOUR support to update and supplement this list. Please supplement if you know more and/or better ones. There are some more converters on the CTAN sites, but the following seem to be most promising for conversion to and from the current versions of wordprocessors.
Neither correctness nor completeness is guaranteed.
All opinions mentioned (if any) are my own. Please send corrections, enhancements and supplements (auch in deutscher Sprache) to the following address:
texconvfaq “at” gmx.de
Note that this FAQ list contains information about converters ONLY between LaTeX and PC word processors. Converters to and from other formats may have own FAQ lists – e.g. see the link for converters to and from HTML.
For the impatient, here is a table with overview of features of the most recent converters.
## General Remarks
Before looking for a converter, stop and think about a principal question:
### What do you want to be converted in which way?
Do you want to convert the document structure, i.e. a heading should remain a heading, a list should remain a list etc., no matter how it will look like in the target format?
Or do you want to convert the appearance, i.e. how it looks like, no matter how it is represented in the target format?
Or do you want a mixture of both?
For using SGML as an intermediate format, you would have to specify the translation rules yourself (as far as I understood). This makes sense, and explains why different people have very different opinions about which converter best fits their needs: They simply have different demands and expectations on what should be converted and how.
So, not only practically there is no converter which is good for everyone and every purpose, but this is even principally impossible because there are no well-defined requirements which a converter should meet.
An additional problem is that TeX/LaTeX can be extended by an unlimited number of macros. Unless the converter contains a full-scale TeX system, it can at best support the publicly available macro commands, not the ones privately written by individual users. Practically you can expect that it supports the standard LaTeX commands and perhaps a few more widely used packages. The only converter which uses a full-scale TeX system is TeX4ht.
So keep this in mind when looking through the following list of converters, try yourself and decide what you need.
### There are several ways to convert.
To illustrate these, let me restrict it to the Microsoft Word case:
• directly type or paste LaTeX code into Word
• use a Word import filter
• use a Word macro: load LaTeX file as plain text, then search for LaTeX markup and replace the markup by formatting, special characters and equations.
• use an external converter:
1. LaTeX -> RTF, then use Word’s own RTF import,
2. LaTeX -> HTML, then use Word’s internet assistant or built-in html converter,
3. maybe other external format(s).
The converters being most complete and currently maintained / supported are:
TeX2Word – a shareware LaTeX import filter for MS Word
GrindEQ – a shareware LaTeX import filter for MS Word
latex2rtf – a free standalone LaTeX -> RTF converter for PC, Macintosh and Unix,
TexPort – a commercial TeX/LaTeX to WordPerfect and Microsoft Word converter for PC.
TeX4ht – a free LaTeX to html or XML converter for PC and Unix produces html which is good for loading into Word. TeX4ht relies on other software, it needs at least a full TeX system.
There are also converters to Powerpoint and to FrameMaker (see further below).
## Directly type or paste LaTeX code into Word
All of these only allow typing or pasting LaTeX coded equations in Word, not LaTeX coded text elements.
“Aurora” (formerly named Ribbit) can now convert a LaTeX coded equation (which must be placed on the Windows clipboard) to Word. The converter is still experimental and as such has a number of limitations, some of which will be addressed in future releases. The converter’s output will generally need some manual touching up to achieve the level of fidelity on a par with the original document.
The other functionality of Aurora, which was the only functionality of its predecessor “Ribbit”, is letting you enter LaTeX equations in word processors such as MS Word or in Powerpoint. One can enter the equation in LaTeX markup, and the formatted equation is inserted as an object.
Aurora needs a working LaTeX installation. If there is no, it will install a micro version of MiKTeX.
“LaTeX in Word”: See homepage (external link) (Freeware, GPL).
It allows to enter LaTeX equations in word processors such as MS Word in LaTeX markup, and the formatted equation is inserted in the Wordprocessor as a png bitmap. It needs a server which performs the conversion. Server installation files are available from the download page (external link).
MathType (external link) allows typing and pasting equations in LaTeX markup.
OpenOffice allows typing equations in LaTeX-like markup.
Word 2007 allows typing equations in LaTeX-like markup (although not 100% compatible), see http://blogs.msdn.com/microsoft_office_word/archive/2006/10/04/Equations-in-Word-2007.aspx
## Use a Word import filter
TeX2Word: Shareware, 99$(45$ academic).
Current version: 2.5, released April 2008.
Support for more document styles and packages will be available with future versions. You can also supply support for document styles, packages and user defined macros by yourself (needs TeX programming knowledge).
Needs:
* MS Windows 95 or later (NT4, ME, Win2000, WinXP),
* MS Word 95 or later (97, 2000, XP) and
* MathType (external link) 4 or later (full version of the Equation Editor which comes with MS Word).
GrindEQ LaTeX-to-Word: Shareware, 99EUR (49EUR academic).
converts LaTeX, AMS-LaTeX, Plain TeX, or AMS-TeX documents to Microsoft Word format.
You can choose the following formats for TeX/LaTeX equations: Microsoft Equation 2007, Microsoft Equation 3.x, or MathType.
Works with Microsoft Word 97/2000/XP/2003/2007 and Microsoft Windows 98/Me/NT/2000/XP/2003/x64/Vista.
Evaluation version is restricted to 10 launches.
## Convert to RTF
### Free:
latex2rtf: LaTeX-to-RTF-converter. See the more detailed page.
## Convert to WordPerfect format
### Commercial:
TexPort converts your TeX and LaTeX files to WordPerfect or Microsoft Word documents.
See more detailed page
## Use a Word macro
### Free:
tex2doc by Thomas Link (external link): LaTeX to WinWord 6 and WinWord 7(95) converter, written as Word macros. Also attempts to convert tables! Not compatible with Word 2000 and up, no further development.
ltx2word, by myself: LaTeX to WinWord 6, WinWord 7(95) and WinWord 97 converter, written as Word macros. No tables. Not compatible with Word 2000 and up, no further development.
See more detailed page.
The following are no full converters but only allow typing or pasting LaTeX code into Word:
“Aurora” (formerly named Ribbit) can now convert LaTeX code (which must be placed on the Windows clipboard) to Word. The converter is still experimental and as such has a number of limitations, some of which will be addressed in future releases. The converter’s output will generally need some manual touching up to achieve the level of fidelity on par with the original document.
The other functionality of Aurora, which was the only functionality of its predecessor “Ribbit”, is letting you enter LaTeX equations in word processors such as MS Word or in Powerpoint. One can enter the equation in LaTeX markup, and the formatted equation is inserted as an object.
Aurora needs a working LaTeX installation. If there is no, it will install a micro version of MiKTeX.
“LaTeX in Word”: It allows to enter equations in word processors such as MS Word in LaTeX markup, and the formatted equation is inserted in the Wordprocessor as a png bitmap. It needs a server which performs the conversion.
See homepage (external link) (Freeware, GPL)
TexPoint enables the easy use of Latex symbols and formulas in Powerpoint presentations. See homepage (external link). (Shareware)
Latest version requires PowerPoint2000, does not work with earlier versions of PowerPoint.
Aurora (formerly named Ribbit) now also supports PowerPoint. See homepage (external link) (Shareware)
## HTML as intermediate format
### LaTeX to HTML
cost free unless otherwise stated
Because HTML is a structured format, the conversion between HTML and LaTeX is rather straightforward. However there remain the limitations of HTML compared to LaTeX, i.e. there are many elements in LaTeX which can not (yet?) be represented in HTML. Converters from LaTeX to HTML are:
Recommended if you have TeX installed or don’t mind to install it: TeX4ht (external link) is a highly configurable TeX-based converter to hypertext. It comes with a built-in default setting for plain TeX, LaTeX and TeXinfo, and it generates html with accompanying css stylesheet, xhtml, or xml. The converter needs a full TeX installation, but this gives the advantage that TeX’s full support for macros and styles is available (with only few exceptions).
Equations are converted to either bitmaps or MathML. There are some different MathML flavors around which can be chosen by an option. (Following description is partially copied from the TeX4ht web site.)
The special command
oolatex
is available for producing xml compatible with OpenOffice (and probably also StarOffice). The output of the command oolatex <filename> is a zipped file with same name and a “.sxw” extension (containing the document in xml format which does not suffer the limitations of html). For this to work, TeX4ht needs a zip program which is not included in the TeX4ht distribution. It can e.g. be downloaded from http://www.info-zip.org/ (external link).
The resulting .sxw file can directly be opened in OpenOffice, converted equations are editable in OpenOffice’s own equation editor. OpenOffice can save the document also in MS Word 97/2000/XP format, but many equations are not correctly converted to Word. This is known to the OpenOffice developers for long, but yet not fixed.
A command of the form
htlatex filename "html,word" "symbol/!"
asks for HTML output tuned toward MicroSoft Word. Such a format, however, relies on bitmaps for mathematical formulas.
Conversion to bitmaps additionally needs Ghostscript and ImageMagic or netpbm.
TTH (external link): LaTeX-to-HTML converter which translates LaTeX into HTML 4.0 markup. Formulae are also translated into standard html markup. (Free for non-commercial applications.)
A sister of tth, TtM (external link), converts formulae to MathML (Linux version for free, Windows version must be paid).
ltoh (external link): LaTeX-to-HTML converter which is highly customizable, i.e. you can define how the LaTeX macros which are used in your document are to be translated. Requires that the input file conforms to LaTeX2e (see documentation). It was last updated 1979, and it seems that the homepage is no longer available, so look on CTAN in …/support/ltoh/ .
HEVEA (external link): LaTeX-to-HTML converter which translates LaTeX into HTML4.0 markup. Formulae are also translated into standard html markup (not yet using MathML).
Hyperlatex (external link) allows the use of a subset of LaTeX to produce documents in HTML .
Some converters are available from CTAN (external link) (“Comprehensive TeX Archive Network”), e.g. in …/support/latex2html.
(The … stands for a host specific base directory, which often is either “/pub/tex” or “/tex-archive”)
### HTML to Wordprocessor
Word 8 (97) and up contain the html converter by default (but its installation may have to be explicitly chosen during the Word setup in user-defined mode).
For Word 6 and 7 (95) for Windows and Mac there are free HTML converters available from Microsoft:
WordPerfect 7 and up have an integrated InternetPublisher.
For WordPerfect 6.1 for Windows, the InternetPublisher is available separately:
OpenOffice can also import html, but much better is using tex4ht for lossless conversion to native OpenOffice format.
## Other intermediate formats
There are ways to use SGML as intermediate format, and others have used it successfully. Having had a quick look at it, I found it rather complicated, especially it seems that you have to define the translation rules yourself. So I did not put more effort in trying to use it. If anyone can give me a ready-to-use cookbook solution, I will include it here.
An upcoming format is XML, a subset of which can be exported and imported by Microsoft Office 2000 and up, OpenOffice uses it as its native format, and the browser programmers are working on implementing XML. It actually is an instance of SGML. As it is more powerful than HTML, conversion from LaTeX to XML would lose much less information than conversion from LaTeX to HTML. There are good chances that it could be used as a general exchange format in the future. TeX4ht already has scripts for converting to XML (TEI or DOCBOOK). MS Word 2000 and earlier can not import XML, for these target systems convert to html+css using the xwtex and xwlatex scripts. MS Word 2003 can export and import XML, but I haven’t yet tested whether it can import the TEI or DOCBOOK files produced by TeX4ht.
The most successful path is using TeX4ht to convert to the OpenOffice format (.sxw, which actually is a zip compressed archive containing the document and vector graphics as XML and the bitmap graphics as bitmap files) and open this in OpenOffice. One could stop there, as OpenOffice is publicly available, or go on and save from OpenOffice as a “MS Word 97/2000/XP” file.
Most astonishing, one could also use PDF as intermediate format. Generating PDF from LaTeX is straightforward if you have a full TeX implementation installed. If you have the full commercial version of Adobe Acrobat 7, you can open the pdf and “save as” e.g. rtf (saving “as Word doc” actually generates an rtf file, too), xml, or plain text. Or you can use other commercial software to convert PDF to Word, just do a www search for “pdf to word” to get several hits. In this path of conversion however the document strucure and probably some formatting will be lost.
Finally, you can use OCR software to convert any printed document to word or plain text. To avoid the inaccuracy introduced by printing to paper and scanning, you can convert the TeX output to ps or pdf, convert this to a bitmap (using ghostscript), and feed this bitmap into the ocr software.
## Convert to FrameMaker
la2mml: converts LaTeX to FrameMaker format. Maybe outdated, latest version was created Nov. 1995.
See more detailed page.
FrameMaker Utilities: Contains converters for both directions (LaTeX <-> FrameMaker) as well as templates which make conversion from Framemaker to LaTeX more easy
This HTML page is part of the texconv pages.
You may copy and redistribute it under the following conditions:
• it must remain intact and the contents unchanged; if you’d like to have something changed, contact me (texconvfaq “at” gmx.de). Reformatting (e.g. from HTML to some other presentation format) is granted as long as the contents are unchanged.
• you may NOT ask money for it except a reasonable cost for media and distribution
## Calculation of Laminar Flow through Fracture
The calculation of laminar flow through fracture is very fundamental (), and it is very important for my research, also. Late last year, I derived the equation for both Newtonian fluid and non-Newtonian fluid by hand. Now I am going to make a note for that derivation for Newtonian fluid, which could be regarded as the answer to an exercise on Transport Phenomena, 2nd Ed. by Bird, R.B., et al., a classical textbook on this topic.
At first we need to describe the physical properties of the fracture model (as shown in Figure.1).
Figure 1. Physical Properties of Fracture Model
A Newtonian fluid is in laminar flow in a narrow slit formed by two parallel walls with length, L, a distance B (fracture width) apart. It is understood that the fracture height, B《W, so that “edge effects” are unimportant. Make a differential momentum balance, and obtain the following expressions for the momentum-flux and velocity distributions:
$\tau_{yz}=\left ( \frac{p_{0}-p_{L}}{L}\right)x$
$v_{z}=\frac{\left (p_{0}-p_{L}\right)B^{2}}{2\mu L}\left [ 1-\left ( \frac{x}{B} \right )^{2} \right ]$
Obtain the slit analog of the Hagen-Poiseuille equation.
$w=\frac{1}{12} \frac{\left (p_{0}-p_{L}\right)B^{3}W\rho }{\mu L}$
## Superabsorbent Polymer
Note: In this post, I would like to introduce the superabsorbent polymer (SAP),which could be used as conformance control agent in oil and gas field. SAPs could absorb and hold a large amount of water or aqueous solutions even under high pressure and high temperature. Just as described in the summary of my proposal, in my research, I mainly test the flow properties of SAP through the fracture or fracture-like model, and the rheological properties with rheometer. Some of the swelling and deswelling behaviors and the effects on the injectivity of SAP through fractures were investigated also. Today SAPs will be introduced in general here. Later, The following context is modified from an unpublished paper by my advisor and me. All rights reserved.
The superabsorbent polymers (SAPs) most commonly available are hard, dry, granular or powdered products made up of a cross-linked polymer with a three dimensional network structure that absorbs and holds a large amount of water and swells up to 200 times its original size and weight in fresh water or aqueous solutions while maintaining its physical structure. [1-4] SAPs are increasingly used in multiple fields of human activity, such as biomedical, agricultural, personal care, and industrial because of its high water absorbing capability. [4-6] Recently, SAPs have been applied in conformance control and water shutoff because they have significant advantages over the bulk gels used in in situ gelling processes, such as controllable size and strength, high chemical and temperature resistance, minimum formation damage, less surface facility requirements, and environmental friendly. [7] Except for the super water absorbency, the mechanical properties of SAPs are very important to the conformance control processes, such as the strength and injectivity. Dynamic mechanical analysis (DMA), rheometry and core flooding experiments are commonly used to determine the mechanical properties. Comparing to core flooding experiments, DMA and rheometry are much more cost-effective.
The SAP used in the research is LiquiBlock™ 40K (40K), a commercial product from Emerging Technology Inc. 40K is crosslinked acrylamide/potassium acrylate copolymer and the major component is 2-Propenoic acid, potassium salt, polymer with 2-proenamide. Its molecular structure is shown in Scheme 1.
Scheme 1. The molecular structure of 2-Propenoic acid, potassium salt, polymer with 2-proenamide.
In preparation for the rheological experiments, preselected dried SAP particles between 20- and 30-mesh were dispersed in 0.05%, 0.25%, 1.00%, and 10.00% sodium chloride solutions for 24 hours to achieve the maximum swelling. Because the density of both dried SAP and swollen SAP is higher than the density of brine, the swollen SAP always precipitated at the bottom of the centrifuge cell. The original and ultimate volumes of SAP in a centrifuge cell were recorded. The swelling ratio of the SAP was calculated from the following equation:
$S_{w}=\frac{V_{s}}{V_{d}}\times 100\%$
where Vs is the volume of swollen SAP and V0 is its original volume. Table 1 shows the ultimate swelling ratios for SAPs in various concentrations of brine.
Table 1. Swelling Ratios for SAP in Brine
Brine Conc. (%) Swelling Ratio (%) Original Dia. (mm) Swollen Dia. (mm) 0.05 20455 0.595-0.841 3.506-4.955 0.25 9659 0.595-0.841 2.730-3.859 1.00 5682 0.595-0.841 2.287-3.233 10.00 3125 0.595-0.841 1.874-2.649
REFERENCES
1. Tang, H. (ChemEOR, Inc.) U.S. USPTO 20,070,204,989
2. Bai, B.; Liu, Y.; Coste, J.-P.; Li, L. SPE Res Eval & Eng 2007, 10, 415-422.
3. Das, M.; Zhang, H.; Kumacheva, E. Annu. Rev. Mater. Res. 2006, 36, 117-144.
4. Buchholz, F. L.; Graham, A. T. In Modern Superabsorbent Polymer Technology; John, Wiley & Sons, Inc.: New York, 1997; chapter 1, 7, pp 22.
5. Raju, K. M.; Raju, M. P.; Mohan, Y. M. Polym. Int. 2003, 52, 768-772.
6. Samchenko, Y. M.; Ul’berg, Z. R.; Komarskii, S. A. Colloid J. 2004, 66, 350-354.
7. Liu, Y.; Bai, B.; Wang, Y. Oil Gas Sci. Technol. – Rev. IFP. 2010. http://ogst.ifp.fr/index.php?option=article&access=standard&Itemid=129&url=/articles/ogst/pdf/first/ogst09046.pdf
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# Differences
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whitepapers:narratives:dq 2012/05/02 11:41 whitepapers:narratives:dq 2013/06/25 14:12 current
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===== Example of Small Group Conversation about Geometric and Algebraic Representations of a Physical Quantity ===== ===== Example of Small Group Conversation about Geometric and Algebraic Representations of a Physical Quantity =====
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This video clip starts at 54:42 and ends at 58:17 in the video 071026Ph422Grp6.mov This video clip starts at 54:42 and ends at 58:17 in the video 071026Ph422Grp6.mov
+
+//This interpretative narrative is based upon a video of the class session and discussions with the instructor and the director of the Physics Paradigms Program, Corinne Manogue, and Len Cerny, a doctoral student. A postdoc, Elizabeth Gire, interacts with a small group in the video. In writing the narrative, Emily van Zee drew upon her research in the tradition of ethnography of communication (Hymes, 1972; Philipsen & Coutu, 2004; van Zee & Minstrell, 1997a,b), a discipline that studies cultures through the language phenomena observed. This interpretative narrative presents an example of students growing into participants in the culture of “thinking like a physicist.”//
+
This narrative presents an example of a small group of three students working together on a large whiteboard on which they have written a complex algebraic expression. One of them draws a geometric representation of a relevant physical quantity and the others try to understand what this drawing means and how it relates to the algebraic expression they have written and the physical quantity it represents. This narrative presents an example of a small group of three students working together on a large whiteboard on which they have written a complex algebraic expression. One of them draws a geometric representation of a relevant physical quantity and the others try to understand what this drawing means and how it relates to the algebraic expression they have written and the physical quantity it represents.
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The students are thinking about how to write a formula for the current density, $J$, of a ring of charge $Q$ and radius $R$ that is spinning with period $T$. The students are thinking about how to write a formula for the current density, $J$, of a ring of charge $Q$ and radius $R$ that is spinning with period $T$.
- +{{whitepapers:narratives:071026ph422photo2.jpg?300 |}}
The algebraic expression they have written for the current density $J$ is: The algebraic expression they have written for the current density $J$ is:
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Seth points again to the same term in the algebraic expression and comments, “That looks,...this to me looks like a $dq$, right?" Seth points again to the same term in the algebraic expression and comments, “That looks,...this to me looks like a $dq$, right?"
-Jack seems to agree, “Oh, OK, yeah,” and then says “$dQ$ over” while writing $dQ$ and drawing a line under the $dQ$ to indicate division. He then points to his diagram while saying, “then our partial length” and finishes with “is going to be $r d(\phi)$” while writing $rd\phi$ under the $dQ$ to form the expression: $\frac{dQ}{r d\phi}$ Jack seems to be expressing orally a clear connection between the visual representation of his drawing and the algebraic expression he is naming as he writes.+Jack seems to agree, “Oh, OK, yeah,” and then says “$dQ$ over” while writing $dQ$ and drawing a line under the $dQ$ to indicate division. He then points to his diagram while saying, “then our partial length” and finishes with “is going to be $r d(\phi)$” while writing $rd\phi$ under the $dQ$ to form the expression: $\frac{dQ}{r d\phi}$Jack seems to be expressing orally a clear connection between the visual representation of his drawing and the algebraic expression he is naming as he writes.
-Apparently associating rd, the length of the arc, with the small charge dQ that would be located there, Seth questions Jack’s algebraic expression, “"So dQ over dQ?"+Apparently associating $rd\phi$, the length of the arc, with the small charge $dQ$ that would be located there, Seth questions Jack’s algebraic expression, “"So $dQ$ over $dQ$?"
-Jack points to the denominator of his expression and names it, “r d (phi).”+Jack points to the denominator of his expression and names it, “$r d (\phi)$.”
-Seth reiterates his understanding that the arc, labeled rd, IS the little piece of charge located there, “But then it...but, like, r d(phi) is dQ, so, like, that'd be dQ over dQ." This is the third iteration by Seth of his understanding that the arc length rd is equal to a charge, dQ, and he uses that understanding to infer an expression that seems to puzzle him, dQ/dQ, which would equal 1 and therefore not be useful.+Seth reiterates his understanding that the arc, labeled $rd\phi$, IS the little piece of charge located there, “But then it...but, like, $r d(\phi)$ is $dQ$, so, like, that'd be $dQ$ over $dQ$." This is the third iteration by Seth of his understanding that the arc length $rd\phi$ is equal to a charge, $dQ$, and he uses that understanding to infer an expression that seems to puzzle him, $dQ/dQ$, which would equal $1$ and therefore not be useful.
-Jack starts to respond, “wait” but is interrupted by Peter, “Uh, that’d be a big R by the way, just (?)..” Although Peter has been restless, reaching for and sipping his drink, and just generally fidgeting, he has apparently been following the discussion enough to notice Jack’s shift from writing capital R to lower case r.+Jack starts to respond, “wait” but is interrupted by Peter, “Uh, that’d be a big $R$ by the way, just (?)..” Although Peter has been restless, reaching for and sipping his drink, and just generally fidgeting, he has apparently been following the discussion enough to notice Jack’s shift from writing capital $R$ to lower case $r$.
-Jack at first defends his choice to shift to a little r, “"Um, well, no, really it has to be a little r, because it's changing” but then reconsiders, “No, wait, no, it's not, it's got to be a big R,...” and changes the lower script r to a capital R in his expression: dQ_ +Jack at first defends his choice to shift to a little $r$, “"Um, well, no, really it has to be a little $r$, because it's changing” but then reconsiders, “No, wait, no, it's not, it's got to be a big $R$,...” and changes the lower script $r$ to a capital $R$ in his expression: $\frac{dQ}{Rd\phi}$
- Rd+
Peter confirms this, “yes” and Jack states, “..because it's not changing" recognizing that the radius of the spinning ring is fixed. Peter confirms this, “yes” and Jack states, “..because it's not changing" recognizing that the radius of the spinning ring is fixed.
The group laughs. Seth commends the exchange, "That was really good intuitive..." and Jack seems about to elaborate when Liz comes by with an open, “How's it going over here?" Jack evaluates their progress, "Not good." The group laughs. Seth commends the exchange, "That was really good intuitive..." and Jack seems about to elaborate when Liz comes by with an open, “How's it going over here?" Jack evaluates their progress, "Not good."
-As Liz moves to the other side of the table where she can read the writing right side up, Seth begins to articulate what they have done so far, “"So we've got, for, J = I times, here's our z component…here's our R component…And we still need our Rd(phi), so we decided that Rd(phi) equals dQ, so we..."+As Liz moves to the other side of the table where she can read the writing right side up, Seth begins to articulate what they have done so far, “"So we've got, for, $J = I$ times, here's our $z$ component…here's our $R$ component…And we still need our $Rd(\phi)$, so we decided that $Rd(\phi)$ equals $dQ$, so we..."
-This is the fourth iteration by Seth of his understanding that the arc Rd equals a charge, dQ, and with the “we decided” he now attributes this understanding to the entire group. Liz interrupts with a “Wait, wait, wait. I am confused…” but does not address this statement. She seems to be reacting to what she is seeing on the whiteboard, the entire algebraic expression that they have written there, rather than what she is hearing in the details of Seth’s explanation.+This is the fourth iteration by Seth of his understanding that the arc $Rd\phi$ equals a charge, $dQ$, and with the “we decided” he now attributes this understanding to the entire group. Liz interrupts with a “Wait, wait, wait. I am confused…” but does not address this statement. She seems to be reacting to what she is seeing on the whiteboard, the entire algebraic expression that they have written there, rather than what she is hearing in the details of Seth’s explanation.
-In watching the video, Len noted that Seth seemed to be still seeing the arc length Rd as being equal to the little charge, dQ, located there. Corinne noted that the issue was not addressed even though he had now made this statement several times within the group and in front of an instructor.+In watching the video, Len noted that Seth seemed to be still seeing the arc length Rd as being equal to the little charge, $dQ$, located there. Corinne noted that the issue was not addressed even though he had now made this statement several times within the group and in front of an instructor.
-Len wondered if Jack is imagining a ghost lambda, is he picturing a Rd? Jack appears to differentiate between the dQ and Rd but his communications back to Seth seem to confirm Seth's equating the two. Corinne commented that this is typical of communications; people hear that part of what someone is saying that confirms what they are thinking and do not necessarily hear nuances that are unrelated to what they are thinking. One of the issues about having students working together in groups is that they are not precise with the language so it is much easier for miscommunications to happen. +Len wondered if Jack is imagining a ghost lambda, is he picturing a $\lambda Rd\phi$? Jack appears to differentiate between the $dQ$ and $Rd\phi$ but his communications back to Seth seem to confirm Seth's equating the two. Corinne commented that this is typical of communications; people hear that part of what someone is saying that confirms what they are thinking and do not necessarily hear nuances that are unrelated to what they are thinking. One of the issues about having students working together in groups is that they are not precise with the language so it is much easier for miscommunications to happen.
-The implications of this are that the students are only beginning to learn how to distinguish between the actual physical thing that they are talking about and the representations of the thing that they are talking about that they are drawing and the algebraic expressions that they are writing down. So “is this physical thing a dQ, which is telling me something about charge? Or is this thing the geometric length Rd?” The students are just not picking up on those nuances very carefully and so even Jack, who drew the original picture and knew that he meant something with a Q, is agreeing to a statement that is just the geometric quantity Rd and Seth is never seeing the difference between them. It is typical of students at this stage, to not distinguish between different physical phenomena that can share the same geometric representation. +The implications of this are that the students are only beginning to learn how to distinguish between the actual physical thing that they are talking about and the representations of the thing that they are talking about that they are drawing and the algebraic expressions that they are writing down. So “is this physical thing a $dQ$, which is telling me something about charge? Or is this thing the geometric length $Rd\phi$?” The students are just not picking up on those nuances very carefully and so even Jack, who drew the original picture and knew that he meant something with a $Q$, is agreeing to a statement that is just the geometric quantity $Rd\phi$ and Seth is never seeing the difference between them. It is typical of students at this stage, to not distinguish between different physical phenomena that can share the same geometric representation.
-Corinne commented that her extended research group has been having a running discussion about whether or not it is a good idea pedagogically to use the symbol dQ or dM to represent a small amount of charge or a small amount of mass. One argument goes that if you have an extended charge distribution and you want to know what the total charge is you should write down for the students Q equals the integral of dQ so that the total charge is the sum of a bunch of little charges. Some people in the group believe that writing that down would help students understand that they have to chop up something large and then sum up the pieces. +Corinne commented that her extended research group has been having a running discussion about whether or not it is a good idea pedagogically to use the symbol $dQ$ or $dM$ to represent a small amount of charge or a small amount of mass. One argument goes that if you have an extended charge distribution and you want to know what the total charge is you should write down for the students $Q$ equals the integral of $dQ$ so that the total charge is the sum of a bunch of little charges. Some people in the group believe that writing that down would help students understand that they have to chop up something large and then sum up the pieces.
- +
-Other people in the group believe that the symbol d should be reserved for things that are differentials in the precise mathematical sense. dQ is not the differential of anything and so they do not want that written down. This particularly rears its ugly head with the switch over to thermodynamics and the students need to distinguish between things that are exact differentials like dU for the internal energy versus things that are not exact differentials like d(slash)Q or d(slash)W or the heat or the work. This distinction is so important that the d(slash) symbol has been developed. Her personal view in these slightly lower level courses has been to emphasize that what one is chopping up is always physical space and that one then adds up some physical quantity on that little chopped up piece so that in this case she would always write Q = integral of Rd. She has been on the fence about using dQ explicitly because she has always felt like it would help some people and make it worse for other people. So this is a video clip where one student is spontaneously using dQ probably because it has been used by either his high school or intro course teachers, it is a common symbol, and it totally confuses one of the other students in this group. Now we have some actual evidence about what happens to students around this question.+
+Other people in the group believe that the symbol d should be reserved for things that are differentials in the precise mathematical sense. $dQ$ is not the differential of anything and so they do not want that written down. This particularly rears its ugly head with the switch over to thermodynamics and the students need to distinguish between things that are exact differentials like $dU$ for the internal energy versus things that are not exact differentials like FIXME d(slash)Q or d(slash)W or the heat or the work. This distinction is so important that the d(slash) symbol has been developed. Her personal view in these slightly lower level courses has been to emphasize that what one is chopping up is always physical space and that one then adds up some physical quantity on that little chopped up piece so that in this case she would always write $Q$ = integral of $\lambda Rd\phi$. She has been on the fence about using $dQ$ explicitly because she has always felt like it would help some people and make it worse for other people. So this is a video clip where one student is spontaneously using $dQ$ probably because it has been used by either his high school or intro course teachers, it is a common symbol, and it totally confuses one of the other students in this group. Now we have some actual evidence about what happens to students around this question.
+**References**
T. J. Bing, Ph.D. thesis, University of Maryland, 2008, http://www.physics.umd.edu/perg/dissertations/Bing/ T. J. Bing, Ph.D. thesis, University of Maryland, 2008, http://www.physics.umd.edu/perg/dissertations/Bing/
+
+Hymes, D. (1972). Models for the interaction of language and social life. In J. Gumperz & D. Hymes (Eds.), Directions in sociolinguistics: The ethnography of communication (pp. 35-71). New York: Holt, Rinehart & Winston.
+
+Philipsen, G. & Coutu, L. (2004). The Ethnography of Speaking. In K. L. Fitch & R. E. Sanders (Eds.), Handbook of language and social interaction (pp.l 355-380. Mahwah, NJ: Lawrence Erlbaum.
+
+van Zee, E. H. & Minstrell, J. (1997a). Reflective discourse: Developing shared understandings in a high school physics classroom. International Journal of Science Education, 19, 209-228.
+
+van Zee, E. H. & Minstrell, J. (1997b). Using questioning to guide student thinking. The Journal of the Learning Sciences, 6, 229-271.
+
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2019-12-13 10:56:47
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http://peeterjoot.com/2022/09/
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## C++ compiler diagnostic gone horribly wrong: error: explicit specialization in non-namespace scope
Here is a g++ error message that took me an embarrassingly long time to figure out:
In file included from /home/llvm-project/llvm/lib/IR/Constants.cpp:15:
/home/llvm-project/llvm/lib/IR/LLVMContextImpl.h:447:11: error: explicit specialization in non-namespace scope ‘struct llvm::MDNodeKeyImpl<llvm::DIBasicType>’
template <> struct MDNodeKeyImpl<DIStringType> {
^
This is the code:
template <> struct MDNodeKeyImpl<DIStringType> {
unsigned Tag;
MDString *Name;
uint64_t SizeInBits;
uint32_t AlignInBits;
unsigned Encoding;
This specialization isn’t materially different than the one that preceded it:
template <> struct MDNodeKeyImpl<DIBasicType> {
unsigned Tag;
MDString *Name;
MDString *PictureString;
uint64_t SizeInBits;
uint32_t AlignInBits;
unsigned Encoding;
unsigned Flags;
Optional<DIBasicType::DecimalInfo> DecimalAttrInfo;
MDNodeKeyImpl(unsigned Tag, MDString *Name, MDString *PictureString,
uint64_t SizeInBits, uint32_t AlignInBits, unsigned Encoding,
unsigned Flags,
Optional<DIBasicType::DecimalInfo> DecimalAttrInfo)
: Tag(Tag), Name(Name), PictureString(PictureString),
SizeInBits(SizeInBits), AlignInBits(AlignInBits), Encoding(Encoding),
Flags(Flags), DecimalAttrInfo(DecimalAttrInfo) {}
MDNodeKeyImpl(const DIBasicType *N)
: Tag(N->getTag()), Name(N->getRawName()), PictureString(N->getRawPictureString()), SizeInBits(N->getSizeInBits()),
AlignInBits(N->getAlignInBits()), Encoding(N->getEncoding()),
Flags(N->getFlags(), DecimalAttrInfo(N->getDecimalInfo()) {}
bool isKeyOf(const DIBasicType *RHS) const {
return Tag == RHS->getTag() && Name == RHS->getRawName() &&
PictureString == RHS->getRawPictureString() &&
SizeInBits == RHS->getSizeInBits() &&
AlignInBits == RHS->getAlignInBits() &&
Encoding == RHS->getEncoding() && Flags == RHS->getFlags() &&
DecimalAttrInfo == RHS->getDecimalInfo();
}
unsigned getHashValue() const {
return hash_combine(Tag, Name, SizeInBits, AlignInBits, Encoding);
}
};
However, there is an error hiding above it on this line:
Flags(N->getFlags(), DecimalAttrInfo(N->getDecimalInfo()) {}
i.e. a single missing brace in the initializer for the Flags member, a consequence of a cut and paste during rebase that clobbered that one character, when adding a comma after it.
It turns out that the compiler was giving me a hint that something was wrong before this in the message:
error: explicit specialization in non-namespace scope
as it states that the scope is:
‘struct llvm::MDNodeKeyImpl’
which is the previous class definition. Inspection of the code made me think that the scope was ‘namespace llvm {…}’, and I’d gone looking for a rebase error that would have incorrectly terminated that llvm namespace scope. This is a classic example of not paying enough attention to what is in front of you, and going off looking based on hunches instead. I didn’t understand the compiler message, but in retrospect, non-namespace scope meant that something in that scope was incomplete. The compiler wasn’t smart enough to tell me that the previous specialization was completed due to the missing brace, but it did tell me that something was wrong in that previous specialization (which was explicitly named), and I didn’t look at that because of my “what the hell does that mean” reaction to the compilation error message.
In this case, I was building on RHEL8.3, which uses an ancient GCC toolchain. I wonder if newer versions of g++ fare better (i.e.: a message like “possibly unterminated brace on line …” would have been much nicer)? I wasn’t able to try with clang++ as I was building llvm+clang+lldb (V14), and had uninstalled all of the llvm related toolchain to avoid interference.
## More “interesting” electrical.
September 17, 2022 Home renos
We naively thought we could swap a couple of sconce lights, but this is what we found
Neither of the existing lights was mounted in a box, instead there was a “clever” surface mounting method used, with the wires and marrettes tucked into little cavities. I see why this was done, especially on the exterior wall, since there is not enough space for a standard size octagon box between the brick and the drywall. We have about a one inch gap, then lathe, then the drywall.
I’ll see if I can find and install a shallow octagon box instead. It will be tricky to do so, because there are no studs to connect to, and not enough space to retrofit any into the wall. As Sofia said, “nothing is ever easy, is it.”
## Motivation
In a discord thread on the bivector group (a geometric algebra group chat), MoneyKills posts about trouble he has calculating the correct expression for the angular momentum bivector or it’s dual.
This blog post is a more long winded answer than my bivector response and includes this calculation using both cylindrical and spherical coordinates.
## Cylindrical coordinates.
The position vector for any point on a plane can be expressed as
\label{eqn:amomentum:20}
\Br = r \rcap,
where $$\rcap = \rcap(\phi)$$ encodes all the angular dependence of the position vector, and $$r$$ is the length along that direction to our point, as illustrated in fig. 1.
fig. 1. Cylindrical coordinates position vector.
The radial unit vector has a compact GA representation
\label{eqn:amomentum:40}
\rcap = \Be_1 e^{i\phi},
where $$i = \Be_1 \Be_2$$.
The velocity (or momentum) will have both $$\rcap$$ and $$\phicap$$ dependence. By chain rule, that velocity is
\label{eqn:amomentum:60}
\Bv = \dot{r} \rcap + r \dot{\rcap},
where
\label{eqn:amomentum:80}
\begin{aligned}
\dot{\rcap}
&= \Be_1 i e^{i\phi} \dot{\phi} \\
&= \Be_2 e^{i\phi} \dot{\phi} \\
&= \phicap \dot{\phi}.
\end{aligned}
It is left to the reader to show that the vector designated $$\phicap$$, is a unit vector and perpendicular to $$\rcap$$ (Hint: compute the grade-0 selection of the product of the two to show that they are perpendicular.)
We can now compute the momentum, which is
\label{eqn:amomentum:100}
\Bp = m \Bv = m \lr{ \dot{r} \rcap + r \dot{\phi} \phicap },
and the angular momentum bivector
\label{eqn:amomentum:120}
\begin{aligned}
L
&= \Br \wedge \Bp \\
&= m \lr{ r \rcap } \wedge \lr{ \dot{r} \rcap + r \dot{\phi} \phicap } \\
&= m r^2 \dot{\phi} \rcap \phicap.
\end{aligned}
This has the $$m r^2 \dot{\phi}$$ magnitude that the OP was seeking.
## Spherical coordinates.
In spherical coordinates, our position vector is
\label{eqn:amomentum:140}
\Br = r \lr{ \Be_1 \sin\theta \cos\phi + \Be_2 \sin\theta \sin\phi + \Be_3 \cos\theta },
as sketched in fig. 2.
fig. 2. Spherical coordinates.
We can factor this into a more compact representation
\label{eqn:amomentum:160}
\begin{aligned}
\Br
&= r \lr{ \sin\theta \Be_1 (\cos\phi + \Be_{12} \sin\phi ) + \Be_3 \cos\theta } \\
&= r \lr{ \sin\theta \Be_1 e^{\Be_{12} \phi } + \Be_3 \cos\theta } \\
&= r \Be_3 \lr{ \cos\theta + \sin\theta \Be_3 \Be_1 e^{\Be_{12} \phi } }.
\end{aligned}
It is useful to name two of the bivector terms above, first, we write $$i$$ for the azimuthal plane bivector sketched in fig. 3.
Spherical coordinates, azimuthal plane.
\label{eqn:amomentum:180}
i = \Be_{12},
and introduce a bivector $$j$$ that encodes the $$\Be_3, \rcap$$ plane as sketched in fig. 4.
Spherical coordinates, “j-plane”.
\label{eqn:amomentum:200}
j = \Be_{31} e^{i \phi}.
Having done so, we now have a compact representation for our position vector
\label{eqn:amomentum:220}
\begin{aligned}
\Br
&= r \Be_3 \lr{ \cos\theta + j \sin\theta } \\
&= r \Be_3 e^{j \theta}.
\end{aligned}
This provides us with a nice compact representation of the radial unit vector
\label{eqn:amomentum:240}
\rcap = \Be_3 e^{j \theta}.
Just as was the case in cylindrical coordinates, our azimuthal plane unit vector is
\label{eqn:amomentum:280}
\phicap = \Be_2 e^{i\phi}.
Now we want to compute the velocity vector. As was the case in cylindrical coordinates, we have
\label{eqn:amomentum:300}
\Bv = \dot{r} \rcap + r \dot{\rcap},
but now we need the spherical representation for the $$\rcap$$ derivative, which is
\label{eqn:amomentum:320}
\begin{aligned}
\dot{\rcap}
&=
\PD{\theta}{\rcap} \dot{\theta} + \PD{\phi}{\rcap} \dot{\phi} \\
&=
\Be_3 e^{j\theta} j \dot{\theta} + \Be_3 \sin\theta \PD{\phi}{j} \dot{\phi} \\
&=
\rcap j \dot{\theta} + \Be_3 \sin\theta j i \dot{\phi}.
\end{aligned}
We can reduce the second multivector term without too much work
\label{eqn:amomentum:340}
\begin{aligned}
\Be_3 j i
&=
\Be_3 \Be_{31} e^{i\phi} i \\
&=
\Be_3 \Be_{31} i e^{i\phi} \\
&=
\Be_{33112} e^{i\phi} \\
&=
\Be_{2} e^{i\phi} \\
&= \phicap,
\end{aligned}
so we have
\label{eqn:amomentum:360}
\dot{\rcap}
=
\rcap j \dot{\theta} + \sin\theta \phicap \dot{\phi}.
The velocity is
\label{eqn:amomentum:380}
\Bv = \dot{r} \rcap + r \lr{ \rcap j \dot{\theta} + \sin\theta \phicap \dot{\phi} }.
Now we can finally compute the angular momentum bivector, which is
\label{eqn:amomentum:400}
\begin{aligned}
L &=
\Br \wedge \Bp \\
&=
m r \rcap \wedge \lr{ \dot{r} \rcap + r \lr{ \rcap j \dot{\theta} + \sin\theta \phicap \dot{\phi} } } \\
&=
m r^2 \rcap \wedge \lr{ \rcap j \dot{\theta} + \sin\theta \phicap \dot{\phi} } \\
&=
m r^2 \gpgradetwo{ \rcap \lr{ \rcap j \dot{\theta} + \sin\theta \phicap \dot{\phi} } },
\end{aligned}
which is just
\label{eqn:amomentum:420}
L =
m r^2 \lr{ j \dot{\theta} + \sin\theta \rcap \phicap \dot{\phi} }.
I was slightly surprised by this result, as I naively expected the cylindrical coordinate result. We have a $$m r^2 \rcap \phicap \dot{\phi}$$ term, as was the case in cylindrical coordinates, but scaled down with a $$\sin\theta$$ factor. However, this result does make sense. Consider for example, some fixed circular motion with $$\theta = \mathrm{constant}$$, as sketched in fig. 5.
fig. 5. Circular motion for constant theta
The radius of this circle is actually $$r \sin\theta$$, so the total angular momentum for that motion is scaled down to $$m r^2 \sin\theta \dot{\phi}$$, smaller than the maximum circular angular momentum of $$m r^2 \dot{\phi}$$ which occurs in the $$\theta = \pi/2$$ azimuthal plane. Similarly, if we have circular motion in the “j-plane”, sketched in fig. 6.
fig. 6. Circular motion for constant phi.
where $$\phi = \mathrm{constant}$$, then our angular momentum is $$L = m r^2 j \dot{\theta}$$.
## Scary electrical… What could go wrong?
September 4, 2022 Home renos
Unplugged an A/C adapter and found this hiding behind it.
Why not just open the box and connect the wire properly? This is right under the electrical panel, so the shutoff for the circuit isn’t far away.
|
2022-12-01 11:03:54
|
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|
https://infoscience.epfl.ch/record/263956?ln=en
|
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### Abstract
This thesis is dedicated to the study of various aspects of the electronic structure of two-dimensional transition metal dichalcogenides (TMDs) of chemical composition MX$_2$ (where M is a transition metal atom and X= S, Se, Te), using a combination of \textit{ab inito} density-functional methods. We first address the relative stability of the $1T$ and $1H$ phases of two-dimensional TMDs as a function of the column of the transition metal atom in the periodic table. Using a Wannier-function approach, we calculate crystal field and ligand field parameters for a broad range of members of this family of materials. Taking TaS$_2$ as an example, we show how the splitting of the $d$ electron states arises from an interplay of electrostatic effects and hybridization with the ligands' $s$, $p$ and $d$ states. We show that the ligand field alone cannot explain the stabilization of the $1H$ polymorph for $d^1$ and $d^2$ TMDs, and that band structure effects are dominant. We present trends of the calculated parameters across the periodic table, and argue that these allow developing simple chemical intuition. Secondly, we study the occurrence of charge density wave phases and periodic lattice distortion in metallic $1T$ transition metal dichalcogenides. The phonon dispersion and fermiology of representative examples with different $d$ electron counts are studied as a function of doping. Two qualitatively different behaviours are found as a function of the filling of the $t_{2g}$ subshell. We argue that away from half-filling, weak-coupling nesting arguments are a useful starting point for understanding, whereas closer to half-filling a strong-coupling real-space picture is more correct. Using Wannier functions, it is shown that strong metal-metal bonds are formed and that simple bond-counting arguments apply. Thirdly, the recently synthesized $1T$ phase of NbSe$_2$, in monolayer form, is investigated from first principles. We find that $1T$-NbSe$_2$ is unstable towards the formation of an incommensurate charge density wave phase, whose periodicity can be understood from the Fermi surface topology. We investigate different scenarios for the experimentally observed superlattice and insulating behaviour, and conclude that the star-of-David phase is the most stable commensurate charge density wave phase. We study the electronic properties of the star-of-David phase at various levels of theory and confirm its Mott insulating character, as speculated and in analogy with TaS$_2$. The Heisenberg exchange couplings are found to be ferromagnetic, which suggests a parallel with the so-called flat-band ferromagnetism in certain multiband Hubbard models. Finally, we address the possibility of the occurrence of the excitonic insulator phase in single-layer TiSe$_2$. The relative role of electron-electron and electron-phonon interactions in driving the charge density wave in layered and two-dimensional TiSe$_2$ has been disputed and is still unresolved. We calculate the electronic structure and finite-momentum exciton spectrum from hybrid density functional theory. We find that in a certain range of parameters, excitonic effects are strong and the material is close to a pure excitonic insulator instability. A possible necessary condition for the physical realization of a pure excitonic insulator is proposed.
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2021-06-21 17:55:01
|
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|
https://www.everythingmaths.co.za/science/grade-10/10-sound/10-sound-08.cnxmlplus
|
You are here: Home End of chapter exercises
## End of chapter exercises
Choose a word from column B that best describes the concept in column A.
Column A Column B 1. pitch of sound A. amplitude 2. loudness of sound B. frequency 3. quality of sound C. speed D. waveform
Pitch of Sound: Frequency
loudness of sound: Amplitude
quality of sound: waveform
A tuning fork, a violin string and a loudspeaker are producing sounds. This is because they are all in a state of:
1. compression
2. rarefaction
3. rotation
4. tension
5. vibration
e.
vibration
What would a drummer do to make the sound of a drum give a note of lower pitch?
1. hit the drum harder
2. hit the drum less hard
3. hit the drum near the edge
4. loosen the drum skin
5. tighten the drum skin
e.
loosen the drum skin
What is the approximate range of audible frequencies for a healthy human?
1. 0,2 Hz $→$ 200 Hz
2. 2 Hz $→$ 2000 Hz
3. 20 Hz $→$ 20 000 Hz
4. 200 Hz $→$ 200 000 Hz
5. 2000 Hz $→$ 2 000 000 Hz
e.
20 Hz → 20 000 Hz
X and Y are different wave motions. In air, X travels much faster than Y but has a much shorter wavelength. Which types of wave motion could X and Y be?
X Y 1. microwaves red light 2. radio infra red 3. red light sound 4. sound ultraviolet 5. ultraviolet radio
c.
red light, sound
Astronauts are in a spaceship orbiting the moon. They see an explosion on the surface of the moon. Why can they not hear the explosion?
1. explosions do not occur in space
2. sound cannot travel through a vacuum
3. sound is reflected away from the spaceship
4. sound travels too quickly in space to affect the ear drum
5. the spaceship would be moving at a supersonic speed
e.
sound cannot travel through a vacuum
A man stands between two cliffs as shown in the diagram and claps his hands once.
Assuming that the velocity of sound is 330 m·s−1, what will be the time interval between the two loudest echoes?
1. 1 s
c.
1/3 s
A dolphin emits an ultrasonic wave with frequency of 0,15 MHz. The speed of the ultrasonic wave in water is 1500 m·s−1. What is the wavelength of this wave in water?
1. 0,1 mm
2. 1 cm
3. 10 cm
4. 10 m
5. 100 m
e.
10 cm
The amplitude and frequency of a sound wave are both increased. How are the loudness and pitch of the sound affected?
loudness pitch A increased raised B increased unchanged C increased lowered D decreased raised E decreased lowered
a.
Increased raised
A jet fighter travels slower than the speed of sound. Its speed is said to be:
1. Mach 1
2. supersonic
3. subsonic
4. hypersonic
5. infrasonic
e.
subsonic
A sound wave is different from a light wave in that a sound wave is:
1. produced by a vibrating object and a light wave is not.
2. not capable of travelling through a vacuum.
3. not capable of diffracting and a light wave is.
4. capable of existing with a variety of frequencies and a light wave has a single frequency.
d.
not capable of traveling through a vacuum.
At the same temperature, sound waves have the fastest speed in:
1. rock
2. milk
3. oxygen
4. sand
d.
rock
Two sound waves are travelling through a container of nitrogen gas. The first wave has a wavelength of 1,5 m, while the second wave has a wavelength of 4,5 m. The velocity of the second wave must be:
1. $1 9$ the velocity of the first wave.
2. $1 3$ the velocity of the first wave.
3. the same as the velocity of the first wave.
4. three times larger than the velocity of the first wave.
5. nine times larger than the velocity of the first wave.
e.
the same as the velocity of the first wave.
A lightning storm creates both lightning and thunder. You see the lightning almost immediately since light travels at 3 × 108 m·s−1. After seeing the lightning, you count 5 s−1 and then you hear the thunder. Calculate the distance to the location of the storm.
Assuming the speed of sound is ,
$d=v×t$ $=340×5$
A person is yelling from a second story window to another person standing at the garden gate, 50 m away. If the speed of sound is 344 m·s−1, how long does it take the sound to reach the person standing at the gate?
$t=\frac{d}{v}$ $=\frac{50}{344}$
Person 1 speaks to person 2. Explain how the sound is created by person 1 and how it is possible for person 2 to hear the conversation.
When person 1 speaks, their vocal chords vibrate, creating identical vibrations in the air. These vibrations, or sound waves, travel through the air and reach person 2. The vibrations in the air causes person 2's eardrums to vibrate and therefore person 2 will hear them.
Sound cannot travel in space. Discuss what other modes of communication astronauts can use when they are outside the space shuttle?
Sound cannot travel in a vacuum. Astronauts may use any other mode of communication that may operate in a vacuum. One method is the use of radios. Radios use electromagnetic waves to send and receive signals and these are able to propagate in a vacuum. If the astronauts' radios fail, they are able to communicate using hand signals.
An automatic focus camera uses an ultrasonic sound wave to focus on objects. The camera sends out sound waves which are reflected off distant objects and return to the camera. A sensor detects the time it takes for the waves to return and then determines the distance an object is from the camera. If a sound wave (speed $=$ 344 m·s−1) returns to the camera 0,150 s after leaving the camera, how far away is the object?
The sound wave travels to the object and back to the camera in 0.15 seconds. Therefore, the distance to the object is:
$d=v×t$ $=344×\left(\frac{0,15}{2}\right)$
Calculate the frequency (in Hz) and wavelength of the annoying sound made by a mosquito when it beats its wings at the average rate of 600 wing beats per second. Assume the speed of the sound waves is 344 m·s−1.
Wavelength:
$\lambda =\frac{v}{f}$ $=\frac{344}{600}$
Frequency:
It beats it wings 600 times per second, therefore the frequency of the sound is 600 Hz.
How does halving the frequency of a wave source affect the speed of the waves?
The frequency and velocity is independent in homogeneous mediums. Therefore, halving the frequency will not affect the speed of the waves, but it will increase their wavelengths by a factor of 2.
Humans can detect frequencies as high as 20 000 Hz. Assuming the speed of sound in air is 344 m·s−1, calculate the wavelength of the sound corresponding to the upper range of audible hearing.
$\lambda =\frac{v}{f}$ $=\frac{344}{20000}$
An elephant trumpets at 10 Hz10 Hz. Assuming the speed of sound in air is 344 m·s−1, calculate the wavelength of this infrasonic sound wave made by the elephant.
$\lambda =\frac{v}{f}$ $=\frac{344}{10}$
A ship sends a signal out to determine the depth of the ocean. The signal returns 2,5 seconds later. If sound travels at 1450 m·s−1 in sea water, how deep is the ocean at that point?
The sound wave travels to the bottom and back to the ship in 2.5 seconds. Therefore, the distance to the bottom is:
$d=v×t$ $=1450×\left(\frac{2,5}{2}\right)$
A person shouts at a cliff and hears an echo from the cliff 1 s later. If the speed of sound is 344 m·s−1, how far away is the cliff?
$\text{The sound wave is heard after 1 s, therefore the soundwave reached the cliff after 0.5s}$ $d=v×t$ $d=344×0.5$ $d=172m$
Select a word from Column B that best fits the description in Column A:
Column A Column B 1. waves in the air caused by vibrations A. longitudinal waves 2. waves that move in one direction, but medium moves in another B. frequency 3. waves and medium that move in the same direction C. period 4. the distance between consecutive points of a wave which are in phase D. amplitude 5. how often a single wavelength goes by E. sound waves 6. half the difference between high points and low points of waves F. standing waves 7. the distance a wave covers per time interval G. transverse waves 8. the time taken for one wavelength to pass a point H. wavelength I. music J. sounds K. wave speed
1. E. (waves in the air caused by vibrations: sound waves)
2. G. (waves that move in one direction, but medium moves in another: transverse waves)
3. H. (the distance between consecutive points of a wave which are in phase: wavelength)
4. B. (how often a single wavelength goes by: frequency)
5. D. (half the difference between high points and low points of waves: amplitude)
6. K. (the distance a wave covers per time interval: wave speed)
7. C. (the time taken for one wavelength to pass a point: period)
|
2017-07-22 11:00:13
|
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|
http://scicomp.stackexchange.com/questions/3062/visualizing-discontinuous-galerkin-finite-element-data
|
# Visualizing discontinuous Galerkin/finite element data
I would like to visualize simulation results, obtained using the discontinuous Galerkin (DG) approach, within ParaView. Similarly to finite volume methods, the problem domain is divided into cube-shaped cells ("elements"). As opposed to finite volume methods, within each cell there is not just one value for the solution vector $\mathbf{u}$, but each cell contains the solution $\mathbf{u}$ at multiple Gauss integration points.
My question is whether anyone has experience with visualizing such data efficiently with ParaView/VTK, and what approach you chose to represent the data in VTK. Several possible ways come to my mind, but I do not know which one is the most promising:
(1) Use voxels
Use one voxel for each integration point.
Pro: All plugins that work with the standard VTK unstructured cell types will continue to work without changing anything.
Con: Since the integration points are not distributed evenly, it might be difficult to find the correct location of the vertices. Also, the solution can be defined twice on the cell surfaces, as the DG framework allows discontinuous solutions. Also, the hierarchical information (domain divided into elements, each element contains several points) is lost.
(2) Use polyvertices
Use one vertex per integration point.
Pro: Easiest to implement, easy to specify multiple points at the same location with different solutions.
Con: Capability to visualize data as "cells" is lost, plus the same disadvantages as above.
Use the built-in support for quadrature schemes.
Pro: Rather straightforward implementation, preserves all relations and properties of the original solution.
Con: Since this is a completely new cell type, many (most) of the existing plugins will not work anymore and will probably have to be rewritten.
-
Could someone with editing rights please add the (new) tags paraview, vtk, discontinuous-galerkin? Thank you. – Michael Schlottke Aug 14 '12 at 9:42 Okay, added the tags. – Aron Ahmadia Aug 15 '12 at 12:43 Thank you, @AronAhmadia – Michael Schlottke Aug 16 '12 at 8:37
deal.II uses option (2) for a long time already with very good success. In other words, in 2d, every vertex appears 4 times in the output file which means there is more data to be written but fields can be discontinuous. The only other drawback I am aware of is that some visualization programs can't follow interfaces between cells that don't share vertices when doing streamlines, though today they seem to have become better.
You may also want to look at this entry in our FAQs: http://dealii.sourceforge.net/index.php/Deal.II_Questions_and_Answers#The_graphical_output_files_don.27t_make_sense_to_me_.E2.80.94_they_seem_to_have_too_many_degrees_of_freedom.21
-
Thanks, Wolfgang, this is exactly the kind of answer I was looking for. – Michael Schlottke Aug 16 '12 at 12:46
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2013-05-24 05:55:15
|
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https://math.stackexchange.com/questions/1407606/how-to-interpret-local-minima-of-combinatorial-optimization
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# how to interpret local minima of combinatorial optimization
I am having a difficult time trying to interpret and visualize the local minima of a combinatorial optimization objective function.
Here's a rough sketch of my problem:
I have $m$ points $x_1,\dots,x_m$ in $\mathbb{R}^d$. My objective function is only a function of any $n$ of these points where $n < m$ and $n$ is fixed. The goal is to find the set of poins $x_{i_1},\dots,x_{i_n}$ which minimizes the objective function. We may denote the solution point to the optimization problem by $(x_{i_1},\dots,x_{i_n}).$ The order of these $n$ points is not important and so there are many local minima, assuming it exists.
Clearly, this is a combinatorial optimization problem with $m$ choose $n$ possible combinations for the solution. Thus the set of possible solution points is finite.
What I'm finding hard to grasp is the meaning of a local minima in this context. Suppose that $x^* =(x_{i_1},\dots,x_{i_n})$ is a "local minima". If we are to use the classical definition of local minima, how do we define the neighborhood of $x^*$? Can we ensure that such a neighborhood belongs to the $m$ points where we started with?
Assume that $n = 1$ and $d=2.$How do you plot the objective function if you have discrete inputs?
any insight appreciated!
The definition of "local minimum" you chose is dependent on your choice of optimization algorithm. Your algorithm will naturally group certain configurations together. For example, if your algorithm starts at one configuration, and explores the configurations which differ from that configuration on only one point, then these configurations are neighbors. A local minimum is then any point whose neighbors have a larger objective function.
This is a useful definition, since then local minima again correspond to configurations the algorithm could get "stuck" on.
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2019-09-21 01:06:57
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https://meridian.allenpress.com/jgme/article/5/2/320/200572/Constructing-a-Novel-Simple-LEEP-Training-Model
|
Background
Duty hour restrictions and enhanced focus on patient safety have prompted the development of new instruction models for practice of surgical techniques outside the operating room, including models for teaching loop electrosurgical excisional procedure (LEEP), a common procedure that gynecology residents perform to diagnose and manage cervical disease.
Objective
We sought to develop an inexpensive and reusable training model for guided practice opportunities that will improve gynecology residents' LEEP technique.
Methods
Polyvinyl chloride, foam, and a polish sausage are used to simulate the basic anatomy of the vagina and cervix. A 2-in-diameter polyvinyl chloride pipe and high-density foam are used to create a realistic representation with the sausage simulating the cervix. An electrosurgical pad is attached to the sausage and a standard operating room electrosurgical generator is used.
Results
After a brief lecture and demonstration of the LEEP procedure, gynecology residents are positioned at individual stations. Use of 2 to 3 instructors allows for the provision of directions and feedback to residents as they perform the simulated LEEP. During the last 6 years, this model has continued to improve residents' confidence and skills with the procedure.
Conclusions
An anatomically accurate LEEP model can not only improve resident knowledge, skills, and confidence, but also improve quality and patient safety. This training model allows residents to refine their surgical skills through guided practice and instructors to monitor performance before residents to perform the procedure on patients.
Editor's Note: The online version of this article contains additional photos of the construction of the LEEP training model.
Traditionally, instruction in surgical technique has been conducted in a Halstedian fashion in the operating room, an environment that may prove less than ideal for several reasons. Reductions in resident duty hours and enhanced focus on patient safety have prompted the development of new instruction models for practice of surgical techniques outside the operating room. In addition, the prospect of learning a new procedure on a patient can be intimidating to surgical trainees, including gynecology interns. The Yerkes-Dodson law, a theory endorsed by many educators, states that environments of low or high stress are suboptimal for learning and performance, and most resident programs have developed new models of instruction to allow residents to practice surgical techniques outside of the operating room.
Many “dry lab” methods for surgical techniques have been developed in the past 2 decades. Creativity has led to the use of gelatin molds in instruction on amniocentesis, computer programs for training in laparoscopy and cystoscopy, and animal models in lieu of human patients.1–,3 In addition, written curricula are used to bolster resident knowledge in the basics of surgical skill before performance of procedures in the operating room. Overall, it is thought that simulation and curricula contribute to resident confidence and skill level.4
The loop electrosurgical excisional procedure (LEEP) is the preferred method of diagnosis and treatment of high-grade cervical intraepithelial neoplasia. It is often preferred over a cold knife cone since it affords less blood loss, is performed more quickly, and can be done in an office setting.5 A LEEP procedure can be difficult to teach in the outpatient setting when the patient is awake and able to converse. In addition, operating in a narrow field such as the vagina poses a challenge unique to gynecologists. Cervical procedures such as the LEEP require specific stereotactic skills that can be challenging to learn. As the relative number of LEEPs is decreasing owing to changes in cervical screening and management, the need for simulation training is more important. As patients become increasingly aware of the apprentice system used in training programs, they may experience more anxiety over a resident “practicing” on them. As a consequence, graduate medical education relies increasingly on the use of simulation.6
The LEEP model is built with common and inexpensive items. Construction begins by cutting a 12-cm segment of 2-in-diameter polyvinyl chloride (PVC) pipe with an electrical saw. Next, 2 circular pieces of high-density foam are cut to the same diameter as the PVC pipe and a 3-cm hole is cut in the center of each piece of foam. The pieces of foam are wedged within the PVC pipe approximately 2 cm away from each other and 5 cm away from their respective ends of the exterior PVC pipe. A 3-cm-diameter polish sausage is inserted into the holes in the foam (figure). The sausage serves as a realistic representation of the cervix with the PVC pipe serving as the vaginal sidewalls. The distance between the sausage and PVC pipe simulate the vaginal fornices. Additional photos of the construction of the model are provided as online supplemental material.
FIGURE 1
Common and Inexpensive Items Are Used for Model Construction
FIGURE 1
Common and Inexpensive Items Are Used for Model Construction
Close modal
A pediatric electrosurgical grounding pad is wrapped around the end of the sausage to facilitate the use of an electrosurgical generator. Using a 2×1-cm electrical wire electrode and an electrosurgical generator set to 40/40 cut-coagulation blend, electrocautery is performed and a portion of the “cervix” is removed. The sausage is “reprepped” by cutting off the coagulated end and rewrapping the electrosurgical pad. A stand is also fashioned by cutting a crescent into a 4-in-diameter PVC pipe. The 2-in PVC pipe rests on the crescent PVC pipe for stability. The model can also be modified by using a 3-in PVC pipe, which allows the instructor to more easily monitor the surgeon.
The major benefit of this model is that the materials can be reused. A sufficient amount of PVC pipe and high-density foam to construct 8 models can be purchased at a local hardware store for approximately $60. The electrosurgical unit was a previously used model and can be purchased for$500 to $1,500. The pediatric grounding pads range from$100 to $140. The electric wire loop is priced at approximately$10. The only item that is not reusable is the sausage, which is purchased for approximately \$6.
The simulation session is held in the graduate medical education's simulation training laboratory at the University of Alabama at Birmingham, and all current gynecology interns participate in the session. As a part of a surgical skills curriculum, the instructor begins the session with a 30-minute lecture followed by a demonstration of the LEEP technique. The indications for a LEEP are reviewed as well as the basic steps to the procedure. Each intern is given instructions and receives performance feedback as he or she individually performs the LEEP procedure, using the model.
In addition, the instructor scores the interns by using a 7-item “essential knowledge and skills for LEEP” checklist. The knowledge portion of the checklist includes discussion of correct materials needed for the procedure, the placement of the speculum, the use of cervical staining solution, and the injection of lidocaine/epinephrine. The skills portion of the checklist includes the resident's demonstration of a right-to-left LEEP, description of a top-hat LEEP, and methods for obtaining hemostasis after LEEP. Interns are encouraged to ask questions throughout the session. All 45 interns to date have successfully completed the simulation procedure while under direct supervision of the instructors.
The model has been used for the past 6 years and interns' response in posttraining surveys has been positive and supportive of this simulation training. Respondents report excellent comprehension of the model and decreased anxiety when performing the procedure. Instructors have reported that interns have excellent communication and technical skills when they perform LEEP procedures in the colposcopy clinic.
We acknowledge that a formal assessment with pretest scores compared to posttest scores would provide additional support that this model improves resident education. Our subjective data during 6 years suggests that this LEEP model should continue to be used in our residency training program. We believe that this LEEP model not only improves patient safety and an intern's LEEP skills, but also allows for an assessment of skills in a nonclinical setting.
Our novel LEEP model facilitates resident education in a low-stress, high-yield environment. It is accepted by interns and instructors as an excellent education tool. While a previous model has been described in the literature, it used more expensive and less reusable materials.7 We believe that the use of inexpensive and reusable materials makes the PVC model an ideal tool for teaching gynecology interns the proper technique of the LEEP procedure.
1
Kirby
TO
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TM
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Kilgore
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JM
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A prospective evaluation of a simulator-based laparoscopic training program for gynecology residents
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Zubair
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Goff
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## Author notes
All authors are at the University of Alabama at Birmingham. Christen L. Walters, MD, is a Resident Physician in the Department of Obstetrics and Gynecology; Jenny M. Whitworth, MD, is a Clinical Instructor/Fellow Physician in the Division of Gynecologic Oncology; Sharon L. Tyra, BS, is a Research Assistant in the Department of General Surgery; Julie B. Walsh- Covarrubias, EdD, is an Associate Professor in the Department of Obstetrics and Gynecology; and J. Michael Straughn Jr, MD, is a Professor in the Division of Gynecologic Oncology.
Funding: The authors report no external funding source for this study.
Presented as a poster at the Council on Resident Education in Obstetrics and Gynecology and Association of Professors of Gynecology and Obstetrics Annual Meeting, Orlando, FL, March 5–8, 2008.
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2022-06-25 07:18:23
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https://squanderingti.me/blog/2018/07/16/shippable-datacenter-part-2-security-discussion-and-a-survey-of-secure-boot-options.html
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Let’s talk about security. One of the criteria I wanted to bake into this project early on was security. I’ve worked in security off and on again all over my career. Which I say only to add emphasis that writing about embedded security is extremely obtuse. It exists in a state somewhere between “non- existent” and “imagine Ikea instructions for a car engine.” I struggled for days on how to layout most of this information and I’m still not thrilled with it… so there’s likely going to be a lot of additional writing and probably a revision coming. Anyway, moving right along.
#### Recap
I started with the Raspberry Pi because I knew it would be a good launchpad to do something more interesting and pursue this idea. I got a basic version working as expected. I could manage a Raspberry Pi from a central management machine, up to and including replacing the OS on the unit entirely via the network. Though not exactly how it would work in something like a managed datacenter, the process was remarkably similar.
If you didn’t read the entire previous article, the bootstrapping process goes something like this:
• new machine ARPs for address, DHCP offers a new address along with a ‘next-server’ to begin netbooting over TFTP (maybe PXE)
• PXE, or something behaving like PXE, starts looking for configuration files over TFTP.
• Machine finds a boot configuration and starts booting
• Some sort of inventory + imaging process kicks off and lays down a new OS on the disk
• Maybe some initial configuration is done for “first boot” into the new OS
• Machine is integrated into the fleet
The first thing I should mention is that any compromise of the management network is a total catastrophe. All of these services assume a secure network and provide little-to-no risk mitigation. For instance, if an attacker’s rogue server is simply faster than the management machine you can offer DHCP first and direct all machines to boot whatever you ‘d like. Or, if you have physical access to the SD card in the Raspberry Pi, it doesn’t matter what’s on that SD card because it can just be replaced and the network skipped entirely.
### So why do we care & what’s the difference?
The fundamental difference between a shippable datacenter and a traditional one is physical tamper exposure. A traditional datacenter is a fortress. For example, a provider I worked with recently had five biometric checkpoints between the parking lot and the cage with servers. There was a Mantrap door between the parking lot and the lobby you had to enter just to provide your ID so you could authenticate further. If you were unannounced you never even made it to the lobby. Like the scene from Sneakers: “The whole building says ‘Go Away.’”
Physical attacks against this kind of infrastructure usually involve going for the supply chain. Finding a way to tamper with a device bound for the cage that’s going to ship from a manufacturer directly to the datacenter without crossing the office. While definitely possible, relatively speaking, it’s a very expensive & complicated attack.
This shippable datacenter on the other hand has no fortress. It’s everything moving as a unit over some sort of logistics freighting system. Additionally, the precept was that it’s installed in the field without typical solid infrastructure. The possibility someone would have physical access is significantly higher.
### The Requirements
With this framing, let’s talk about how we can build a more secure architecture to meet our needs. Is there a way we can ensure that these machines only run the system that we want them to run? We have three major concerns right now:
• Attacker replaces SD card
• Attacker places TFTP-capable server on the network and begins offering boot info, system image, etc
• Remote verification/attestation
Phrased differently: Is the boot media in the machine the media I expect? Is the replacement content for that boot media served by the network the content I expect? Can I verify the state of that content at arbitrary points?
The rest of this particular article, and indeed the start of the next several articles, is going to concern a survey of the major secure boot options available.
#### What is secure boot?
I’m going to be slightly reductive and say secure boot is the process where a trusted piece of firmware verifies cryptographic signatures on every successive stage of booting. The firmware verifies the bootloader, and the bootloader verifies the OS.
#### Raspberry Pi (In)Security
While the Raspberry Pi is a superb educational tool and a great prototype platform, it provides absolutely no security. None. If there ‘s even a chance that a system compromise would have negative consequences with real-world fallout, it would be unethical to deploy the Raspberry Pi. Key takeaways, assorted notes, and what I mean by no security:
• The Raspberry Pi bootloader has no notion of authentication. If it finds bootcode.bin and start.elf on the SD card it’s going to boot from it. Similarly, if the unit has been programmed for USB boot it will try the network. If a TFTP server offers bootcode.bin and start.elf it will load those.
• bootcode.bin and start.elf are, themselves, not authenticated. If someone reverse engineers these (currently closed source) they can control the boot process. Since Raspberry Pi technically boots the CPU from the GPU the CPU will start in a potentially unknown state.
• There’s no way to specify the boot order. First thing found offering bootcode.bin and start.elf gets to dictate the rest of the process. SD card is always checked first.
• The SoC (System on a chip) is the Broadcom BCM2837B0. All the security features that exist in the underlying ARM Cortex-A53 cores have been disabled in silicon. https://github.com/christinaa/rpi-open-firmware/issues/37#issuecomment-388551489
• No TPM (trusted platform module) for key storage. Encrypting SD card is useless since it would have to contain the key in plain text for booting. Requiring a password 1) defeats the purpose of remote deployment and 2) lack of something like SOL (Serial over LAN) makes inputting it remotely difficult.
What are the alternatives in the space? Does any single-board computer offer a compelling security story? As of this writing there are a few different competing specifications for implementing secure boot on ARM, or even x86, based architectures.
### The Options (Sort of Specification-wise)
This list, while not exhaustive, covers the major options for securely booting a single board computer (SBC).
• ARM Trusted Firmware / Trusted Board Boot
• High Assurance Boot (Freescale iMX SoCs only)
• U-Boot (Sort of…)
• UEFI Secure Boot
#### ARM Trusted Board Boot (TBB)
Technically this is a thing, but in practice, it’s mostly just a document. ARM’s ecosystem, much like the Android ecosystem, is severely fragmented. ARM manufactures the Cortex series cores that are used in nearly every mainstream SoC available today. Despite those cores implementing the features required to support things like ARM TrustZone and TBB, they require cooperation from both the SoC manufacturer and the SBC manufacturer. The SoC manufacturer has to wire them in and integrate them correctly. The SBC manufacturer has to work with the SoC manufacturer to make sure their bootloader can initialize everything correctly and securely. As you’ll recall, above, I said the Broadcom SoC in the Raspberry Pi has mostly disabled the required security features.
Additionally, before you can have TBB, you must meet TBBR (Trusted Board Boot Requirements)… Which is another onerous specification. So assuming the manufacturer has done everything for TBBR, they can begin cloning+modifying ARM’s TrustedFirmware reference starting point <https://github.com/ARM- software/arm-trusted-firmware> . This reference spec is itself a living breathing thing, so unless a manufacturer is keeping their proprietary fork up to date, as pieces become available in the formal spec, the specific manufacturers firmware releases won’t support them.
A handful of manufacturers exist claiming to offer various levels of implementation of TBB like Xilinx, but finding out if a specific SBC has support is a documentation nightmare. The spec has been around for years, but unless people start clamoring for it, adoption looks like it will remain low. Matteo Carlini has a good presentation at Linaro Connect talking about the spec http://connect.linaro.org/resource/sfo17/sfo17-201/ that also includes mentioning how UEFI (below) can co-exist with it.
Theoretically this specification allows for remote attestation provided that the ARM Trusted Firmware implementation sufficiently implements TrustZone. Unfortunately, given that it’s up to every individual manufacturer, this has to be evaluated on a case-by-case basis.
#### High Assurance Boot
First off, it’s a proprietary option made by Freescale (which merged with NXP and then purchased by Qualcomm, so maybe we’ll see it elsewhere?) and thus only works on boards using the i.MX SoC. Under the hood it works like most of the options out there- whatever you want to boot requires a signature that we validate before execution. What makes HAB nice is that the keys are write- protected behind one-time programmable (OTP) fuses and we can permanently fuse the keys to the board. Others might disagree, but I like this no-take-backsies approach.
Things I’m less fond of:
#### U-Boot (Sort of)
I’m including this, despite it not being a specification, because there’s a handful of devices out there that basically make the pitch “you always have the option of compiling u-boot for your particular board and using that for secure boot.” Unless there’s a way to:
• permanently fuse your compiled version of u-boot with keys into something like onboard SPI flash
• guarantee it’s the only boot option
• make sure it always executes no matter what
… then it’s not much better than the Raspberry Pi option. Secure boot is only viable if the attacker can’t replace the bootloader. This is why Apple pays a \$200K bug bounty on bootloader vulnerabilities.
While it can use a TPM it doesn ‘t require it, so remote attestation remains tenuous.
#### UEFI Secure Boot
In my opinion this is the best option available today. It also has the added benefits of being the de-facto standard on servers for years as well as being the standard advocated for by several industry juggernauts (Microsoft, Intel, HP, etc). UEFI in general has been around for nearly 20 years and has a full ecosystem around it. I’m not sure when secure boot showed up specifically but it was common enough that in 2011 Microsoft was comfortable mandating it as a requirement for installing Windows 8.
Unfortunately, as far as SBCs go, it’s only implemented on a few very select boards, most of which are manufactured by Intel. This is because Tiano, the reference UEFI implementation, is also made by Intel. One major thing to keep in mind: UEFI secure boot requires a TPM to verify the bootloader. So boards like BeagleBoard supporting EDK2/Tiano are available, but actually implementing all of secure boot requires some sort of a DIY TPM add-on.
### The Best Option So Far
Is there a board out there that actually implements a reasonable security story? The best one I’ve managed to locate yet is the Minnowboard Turbot.
It’s manufactured by Intel and uses the reference Tiano/EDK2 UEFI firmware. Additionally, it supports the newer firmware TPM (fTPM) 2 specification so actually includes a proper chain for both making sure the board only boots what we want and verifying the firmware remotely afterward. Surprise surprise, an interesting side note on this one, it ‘s one of the few SBCs that actually doesn ‘t use ARM and uses Intel Atom E3826 or Intel Atom E3845 depending on version.
I’ve gone ahead and setup the dual-core Turbot board. After working with the Raspberry Pi (which I still think is great!), the Turbot feels absolutely luxurious. It more or less boots and behaves like a rack mounted server thanks to the full UEFI implementation. Further, it doesn’t require any special steps in constructing boot media, so using the Ubuntu base server image on USB was seamless. Additionally, getting secure boot working with the fTPM, while not trivial, was at least straightforward.
### Next up!
Next in the sequence I’ll talk about getting the Minnowboard’s UEFI secure boot process setup along with TPM basics so we can start building a closed chain of trust.
If you liked the above and want to see more examples and how they interrelate then this section is for you.
The raw slides from the Linaro Connect presentation
^^ Worth reading to get a grasp of how gnarly these specifications can be on the inside.
Android verified boot
^^ Though it mostly applies to handsets, the underlying tech is very similar. General purpose computers/servers are lagging behind what Android is doing in embedded security.
UEFI and ARM living together discussion
^^ Solid discussion of how they live together and can support one another.
20 ways past secure boot
^^ Fun presentation by Job de Haas on how many ways you can do secure boot incorrectly and render it useless. Great survey of attacks.
Tiano Core, getting started
^^ Provides a great starting place with TianoCore. Particularly interesting if you want to see how the sausage is made regarding UEFI.
Take Control of Your PC with UEFI Secure Boot, Linux journal
^^ Provides an excellent discussion on the individual administrative steps of UEFI and how to do them with OpenSSL.
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https://worldbuilding.stackexchange.com/questions/69255/how-would-a-primitive-society-react-to-a-cataclysmic-event-that-disproves-their
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# How would a primitive society react to a cataclysmic event that disproves their beliefs?
My novel deals with a primitive society, geographically similar to ancient Egypt, based on a planet with rings. The society, known as the Motek, have a very strong sense of order -- everything has a place, very structured society, breaking out of your rightful place is sacrilege, etc.
The reason for this has to do with their origin story: in the beginning, the universe was ruled by Chaos, your usual malevolent force of destruction, and life was rough. The Motek gods came to the rescue, sacrificing their own lives by forcing Chaos off the planet and becoming the rings, which act as a shield against the ever-encroaching Chaos.
At the start of my book, the rings disappear. First, I know this is scientifically improbable, if not impossible. I don't care. Second, remember this isn't just a natural occurrence to the Motek -- the rings aren't just rings, they're actual gods protecting against Chaos.
How would society react? I'm particularly interested in research about this -- there has to be books or articles out there about primitive cultures dealing with the destruction of their beliefs and worldview.
I've imagined the basic pattern -- fear, panic, riots; rebellions; depression and suicide, etc. Any more thoughts? Or any research? I've had ZERO luck googling this!
• I suspect rioting would be very limited, and if it happens, would be very harshly dealt with. At the level of ancient Egypt, most existence is subsistence. To "riot" in such a situation puts the entire society at direct risk. – a CVn Jan 26 '17 at 8:32
• Things to Google: the rise of the Ghost Dance religious movement amongst some Native Americans in response to their way of life being destroyed en.wikipedia.org/wiki/Ghost_Dance . Also you might want to investigate the Aztec/Maya religions which believed they needed to make blood sacrifices to keep the world intact and functioning, but those practices were stamped out by Christians. Also read up on Cargo Cult religions. – DrBob Jan 26 '17 at 15:36
• How did the Catholic Church react to science? First they denied it, then they claimed that was what their scriptures really meant all along. – jamesqf Jan 26 '17 at 18:06
• Although your question can be answered independently of your example, I don't see how the rings disappearing disproves their beliefs. If they think the rings are dead gods, and the rings go away, then the logical conclusion is that the gods came back to life and went off to do something. – DCShannon Jan 26 '17 at 18:51
• What @jamesqf said. People with "beliefs" don't care what evidence you throw at them. Their gods disappear, that doesn't mean they think that their whole religion is wrong, that just means they where "bad" and the gods want to punish them, or something else along that line. – r41n Jan 27 '17 at 10:01
The closest equivalent to this in human culture would be rare astronomical events - supernovas, and to a lesser extent, comets and eclipses. Events such as these have been seen as omens, and in ancient civilizations, an omen could cause a great deal of unrest among a population.
Aside from eclipses, which civilizations had memory of and therefore knew were not necessarily the end of the world, most of these events are minor and only apparent to people who watch the sky on a regular basis - which in ancient civilizations, was typically the clergy. The disappearance of rings, however, would be much more noticeable to the general population.
However, a simple omen, no matter how ominous, will not by itself cause the collapse of a stable civilization. Many people have written of omens that preceded and retroactively predicted cataclysms that came after them, but there is no case of a celestial event causing or even triggering a major social or political event directly, because that simply doesn't happen. The most likely result would be people staring at the sky for a few minutes, walking around in fear for a few days, and the priests coming up with an explanation to calm them down, after which they will return to their daily lives. Perhaps the gods are simply off fighting the Chaos away from the planet, for instance.
People may come up with different explanations and act accordingly, and those explanations will generally be based around whatever they want the omen to mean. If there is already material cause for unrest, it may aggravate that unrest; a revolutionary group may decide it is a sign for them to rise up, but if people are more-or-less okay with their situation things in the sky are not going to concern them excessively.
• The Creation of the Giordano Bruno in 1178 for example (with turned out to not be meteor hitting moon but more like the Chelyabinsk meteor in 2015) – SZCZERZO KŁY Jan 26 '17 at 9:40
• For those interested in a quick fix: en.wikipedia.org/wiki/Giordano_Bruno_%28crater%29 – Mad Physicist Jan 26 '17 at 15:29
• "and the priests coming up with an explanation to calm them down" explaining the unexplainable is after all the primary purpose of religion – Justin Ohms Jan 27 '17 at 0:50
• @JustinOhms I thought it was archiving and disseminating knowledge especially before writing or printing. – djechlin Jan 27 '17 at 17:41
First step: Explain why rings dissapear. At least to yourselves. You do not have to uncover it anywhere in the story, but you should know why it actually happened. For example, I will assume it is astrophysical phenomena similar to Solar eclipse
Second step: Explain how often it can actually happen Continuing the example, observing solar eclipse is very rare. Especially if we are talking about relatively small society located on one place on your planet (my second assumption)
Third step: Explain how long will it take: Under my assumptions, this is "just" natural phenomena which is very rare and happens under specific conditions. Real solar eclipse takes just few hours to observe. Long enough to panic, short to have revolution started. However, if it takes more than day in your example, your people have real problem...
Fourth: Inspire yourselves in existing religions Example with ancient Egypt will work great under my assumptions. Egyptians saw the Sun as the God, so Solar eclipse observed in Egypt had to have huge impact at believers at the time. Explore ancient Egyptian religion and inspire self
## Possible reactions:
1. God has abandoned us. The Chaos is taking on us. This is the end of the world. Abandon all hope
2. God is angry. We need to make [specific religious ritual] in order to make up with Him/Her/It
3. Chaos is taking on the rule now. Abandon the faith and worship Chaos now.
4. Chaos is taking on rule now. We have to keep faith very tightly in order to survive Chaos rule (Lets become religious fanatics in other words)
(and so on)
• I like the idea of using a solar eclipse type event to temporarily hide the rings instead of the unlikely idea of them disappearing. Since the particles around ringed planets are only visible because of light reflecting off of them make the case that light simply isn't hitting them at this time. This allows you to bring them back at the end of the story. – DasBeasto Jan 26 '17 at 14:45
you have an historic example which might answer your question: the Lisbon earthquake
The earthquake had wide-ranging effects on the lives of the populace and intelligentsia. The earthquake had struck on an important religious holiday and had destroyed almost every important church in the city, causing anxiety and confusion amongst the citizens of a staunch and devout Roman Catholic country. Theologians and philosophers focused and speculated on the religious cause and message, seeing the earthquake as a manifestation of divine judgment.
You can easily translate it in your world: you worship Badabup, supreme ruler of the Universe, and he cast his 4 handed blessing on your race because of it. And his blessing includes this event which crumble your city to dust... well, maybe better worshipping somebody else...
How they would react could range from one extreme to the other. For example they could go the seemingly obvious route and say "Our gods have abandoned us!" or "Chaos has taken over and we are doomed!". However, they can also go in the opposite direction as well. For example they could say "Chaos has been vanquished and the gods have moved on/sacrificed themselves".
My thought would be that the events immediately after the rings disappeared would decide how they react. What is also is important is what caused the disappearance as that will change what happens after.
Cause - Natural Phenomenon
Follow up Event - Effects that natural order of the world badly
Examples of how this might effect the world badly is perhaps certain important chemicals or whatever are rained down onto the world from the rings (I dont know the physics behind this or if its even possible or not, just a random thought), or it rains down asteroids on the planets causing widespread damage, tsunamis etc.
They will likely react in a way such that Chaos has taken over and the gods that protect them have abandoned them or are dead.
Follow up Event - Effects that natural order of the world in a good way
Perhaps the rings were affecting the oceans tides and now the water is all extremely calm.
They may now believe that Chaos has been extinguished and only peace reigns supreme. Why did their gods leave? perhaps because they are no longer needed, or they went to fight chaos elsewhere.
Cause - Unnatural Phenomenon (Ex. Aliens)
Follow up Event - Alien Invasion
Following the destruction of the rings which were actually a defensive weapon put in place by another alien race, the alien invasion begins raining down hellfire and absolute destruction.
They will see it as the gods of Chaos literally coming down. They're own gods failed and were destroyed.
Follow up Event - Aliens help them prosper
The aliens, seeing a primitive and helpless society, help them giving them medicines and teaching them how to grow crops more effeciently.
This would be seen as their gods coming down to help them (hence why the rings disappeared)
Cause - Unknown
Follow up Event - Not much
If nothing really happens then after an initial period of some fear and panic, people will go back to living their lives. They may come up with some reason as to why the rings disappeared for example the gods are off fighting elsewhere). Over time the religion would likely become mythology and atheism or a different religion would replace it.
• +1, although it would be good to point out that in none of these scenarios was their belief disproved by the event. They just conclude that additional events have happened in addition to the gods fighting chaos, dying, and becoming the rings. – DCShannon Jan 26 '17 at 18:54
While I am not aware of any research (and I agree it's a challenging question to have google answer) - I can venture my own thoughts on the question you pose.
1st - I think the actual reason for the disappearance of the rings has some relevance. Reason being - if something happens to cause the material of the rings to shift from their orbit - and either fall to the surface creating some kind of insane meteor shower or escape the gravity well with some kind of visible sign this would be observed by the people.
These are their Gods - they will be watching them - and if something happens to them it will be the biggest thing that happens in their generation.
Their Shamans (or whatever you call their spiritual leaders) are extremely likely to come up with some explanation. If they are corrupt and self serving - it will present an opportunity for them to cement (or increase) their own position of power. If they are noble and genuine - they will attempt to craft a story that will cause their people to become better in some way.
2nd - you could always go with the story of the rings being the actual incarnation of the peoples Gods, and they have have decided to wake up and take a direct interest in the world around them. Perhaps because of some corrupt priest they object to or perhaps because of some threat or danger about to materialise which they need to prepare their people for.
• I never even thought about having the rings ACTUALLY be the gods, though that takes this novel distinctly out of the realm of realistic... And as far as the reason, there isn't one... at least not one that I've come up with. The rings do fall to the earth -- in fact, the leader finds one -- but not a lot of them fall on the land where the culture is. – rightangles Jan 26 '17 at 8:42
• Well - not so much really. Even if you don't believe in God yourself - it doesn't stop you from writing a story or world where such a being (or beings) exist. You simply need to provide a logical basis for their inclusion in your world. Sort of along the lines of the current incarnations of the ancients from Stargate... Or come to that - even the Goa'uld themselves from Stargate... – kiltannen Jan 26 '17 at 8:43
• Well - that additional piece of info about the leaders finding a chunk from the rings leans towards the 1st concept I tossed around. So your biggest thought would be ariound are your leaders "good/ altruistic" or are the "evil/ selfish" – kiltannen Jan 26 '17 at 8:51
An alternative angle for googling : destruction of beliefs doesn't necessarily concerns events of astronomical proportion. Being faced with new, unknown cultures and populations in a sudden fashion might also challenge existing beliefs.
Think along the lines of : we were the chosen one, or there is only us on earth and all of a sudden there's others invading us (or the reverse of this, there are new people to invade).
Looking at historical events matching the above might help you model your situation in a realistic fashion.
Jews reacted to diaspora from the promised land by clinging deeply to their beliefs and maintaining their culture intact for millennia. American population went from prosperous empires to dust in no time and dissolved (and surely part of this is due to their reaction to Spaniards invasion). The flip side of this:powerful invading Christians society maintained their beliefs intact and concluded that other races where inferior once discovered.
• The pre-Columbian peoples did have large scale societies but in the vast majority of cases, they were destroyed by new world disease decades or even centuries before any Europeans arrived in the areas where the civilizations had been. Moreover, there simply weren't enough Spaniards to actually carry off an "invasion." Given the tech at the time, the Sp could a couple of hundred effectives at anytime. They empires of millions deploying 10^5 warriors. In all cases, the SP allied themselves with indigenous factions already at war or thinking about it. Recommend 1491 by Charles Mann. – TechZen Jan 27 '17 at 19:29
• Thanks for the reading suggestion. For what I know, Inca's empire was still prosperous and well at the time of Atahualpa. I am by no means an expert, so there are probably more fitting examples than the ones I made. – Three Diag Jan 27 '17 at 19:33
• Cortez actually got his ass kicked by the Mayan kingdom that controlled the area he landed in. Pre-Columbian people's were not stupid or infantile. They were highly sophisticated, especially in politics. By the third battle, the kingdom's warriors had completely adapted to firearms, artillery, horses, dogs ect, and the next fight would have been Cortez's last, but the Mayan Kingdom was a subject of the Aztecs who had turned into the Nazi's of mesoAmerican. The Maya saw in Cortez a potential leader from outside, one who could unite and command subject kingdoms long mistrustful of each other. – TechZen Jan 27 '17 at 19:34
• No quite the opposite, the Inca had just, by weeks or months emerged from a long and bloody civil war at the top and rebellions among subjects. They had already been hit by at least small pox carried along the Inca's massive land and sea trading routes but the civil war was already ongoing. Pizarro, found Inca allies before even entering the empire. The Inca, like the Aztecs, a rigid command and control system making them highly susceptible to decapitation strikes. When Pizarro assassinated the presumed emperor winner of the recent civil war, the whole system Inca collapsed. – TechZen Jan 27 '17 at 19:41
• It's worth noting that when Cortez first arrived at Tenochtitlan, he did so at the head of allied indigenous army of at least 20,000, That more than anything else got the Aztec's attention. When he came back to conquer the city, he had an army of at least 100,000. Sp tech helped provide some critical firepower and engineering at keypoints but it was Cortez's diplomatic skills that really counted. This pattern of Europeans allying in local disputes was the near universal pattern of European expansion everywhere in the world. – TechZen Jan 27 '17 at 19:47
Less of a straight answer, but you should probably ask yourself HOW the disappeared. I don't mean like a scientific explanation, but for of how did it look when it happened? Did they up and vanish? Did they fly away? Did the burst in flames?
All of these would be interpreted differently, and would lead to different reactions. Personally, I would make them fall into the planet. The primitives would see this and interpret that the gods have "fallen", and have possibly even joined them.
Given that the people actually saw their gods defend them, and they are now absent, I would expect the overwhelming response to be one of a continual sense of impending doom. They can clearly see that they are no longer protected, so therefore they are weak and open to be attacked.
This puts people in a "yelling fire in a crowded theater" scenario. Their panicking about possibly dying in the near future will cause their self preservation instinct to kick in, and that in turn detracts from society as it destroys mutual trust between people.
Others might focus more on the gods having forsaken them. Because human opinion is so varied, this will lead to several religious stances:
• The gods are punishing us. We must do away with [current hot topic, e.g. legalizing gay marriage as a good modern day anti-religious example] or we will all die.
• The gods are dead. We are on our own now. Anarchy reigns.
• The gods are dead. We are on our own now. We must defend ourselves.
While not everyone will see it that way, people will adamantly defend it because they believe it. Furthermore, they can actually point to tangible proof, the rings have disappeared.
Look at how zealously religious people can already preach to the world in real life, and realize that none of them have ever laid eyes on the god they worship. Having that tangible bit of proof would drastically exacerbate their zeal.
As to which of the listed opinions (or others) takes the majority of people, I can't say. I don't think even the people could say that, because it depends on some factors:
• The preacher's preaching ability can vastly influence whether people believe them or not.
• Similarly, even if a preacher is completely right, he might not be believed if he had a questionable reputation in the past.
• Coincidental events can lead people to believe a specific preacher. If someone speaks out against the preacher and a lightning bolt strikes him seconds after (through pure coincidence), everyone will believe the preacher.
• There can be established lore that makes a certain scenario more likely. If the scriptures contain earlier stories of the gods punishing humans for their transgressions, it's a lot more believeable that the same thing is happening now.
When you're dealing with religion trying to explain the (to them) unexplainable, you can't really rely on logic to know what will happen. It's much more likely to be a varied spectrum of interpretations (coloured by people's personal opinions and experiences).
As time progresses, someone will invariably appear to be "proven right" even through some stroke of luck or coincidence. If more than one theory ends up being "proven right", then it would divide the populace even more.
I tend to think that religious beliefs are more robust than that. The event you describe doesn't disprove the belief, but it will be interpreted in the terms of whatever systems of belief the people have.
So, the rings (gods) have gone. People will have opinions what this means. Have the gods gone elsewhere? Have they died (I mean, even more so than they were already) or been destroyed? Have they merely changed form, and are still protecting the people but no longer visibly from the sky? Have they been reborn as the individuals they originally were, as opposed to the diffuse rings they became when they sacrificed themselves? If they have gone, does that mean the people are now in grave danger of attack from chaos, or does it rather suggest that the people now have the protection of the ordered social structures developed in the time since the gods great sacrifice, and so the gods no longer need to be there and have left voluntarily? No doubt other interpretations are possible. Some interpretations lead to the logical conclusion that the people should keep doing what they're doing, others lead to the logical conclusion that the people should run around in small circles screaming.
The interpretation that actually prevails might depend on whether the religion has an authority that the people actually trust to determine this kind of thing, or whether each practioner is inclined to draw their own conclusions and then argue their opinion. It will probably depend also on whether chaos is truly considered by the faithful to be a clear and present danger, or a thing of the past.
Athough not so striking as a planetary ring, there are plenty of historical and mythical examples where a community has lost a physical manifestation of the favour and/or protection of the Gods. So for example, when the Trojans lost the Palladium, the city fell to the Greeks, was destroyed, and the people killed, enslaved, and scattered. That was the mythical end of the Trojans, except in that Aeneas' line survived to rule Rome.
So if the people expect something like that to be the result of the rings disappearing then there could well be general despair and unrest. If actual prolems materialise during this time, then the unrest could easily worsen them into existential threats to the society, in which case the expectation of doom could be self-fulfilling.
Conversely, when the Temple in Jerusalem was destroyed, and Moses' Ark lost, this (and surrounding events) hugely affected the material condition of Jewish society. But the fact they had lost an object believed to be the physical presence of God and proof of His covenant with their people, did not dispel their faith that the covenant still exists. At least, not for those who remain faithful.
I would say that if this event does cause the people to cease believing in their religion and their principles of order, then it is because the society was anyway ready to discard that system. If the faith had become largely a matter of civic tradition and going through the motions, then the event might still be very significant politically, since it opens the theocracy to a loss of legitimacy, but to many people the gods themselves would be no great loss. So if revolution was on the cards already, this event could be the trigger for it to happen. The consequences depend on the revolutionaries and how the revolution plays out.
Equally, though, sometimes people fear that a terrible thing will happen, it doesn't happen, and they get on with their lives. "OK, so we don't have the giant sky-shield any more, we must even more be on guard against chaos".
Purely materialistic explanation:
First of all, for the most of history across the world's cultures, the concept of empirical testing of ideas and beliefs simply didn't exist. Truth came from authoritative tradition, not experimentation. It took the West centuries to come around to the idea testing ideas materially and that largely driven by practical needs such a long range navigation and the need to create new technologies. Egyptian civilization existed for longer than all civilization since combined, nearly 5,000 years and they never developed the idea of empiricism.
(Note that empiricism and rationalism are not the same thing. Neo-platonism was highly rational yet rejected empiricism entirely. )
(The evolution of empiricism requires a certain level of technology, especially uniformity in the production of materials used for measuring instruments, more than any philosophical or theological shift. A careful examination of the time lines of technology and measurements reveals that improvements in empirical power generates the philosophical and theological changes that required to justify the continued use of empiricism. Form follows function, which means function preceeds form. Likewise, justification follows utility which means utility precedes justification.)
Astronomy became the first science because its measurements depended on angles, and devices for measuring angles report the same results independent of the materials they were made of e.g. a wood divisor, a stone divisor or metal divisor, all report the same angle even though environmental conditions of heat and humidity cause each class of materials to alter in different axes and different degrees.)
Secondly, religions don't exist to provide explanations of the material world but to provide psychological mechanisms to enforce greater social cooperation and cohesion. The actual various religious stories don't actually matter to the religions survival as long those stories induce adaptive behaviors in their adherents i.e it doesn’t matter whether an individual refrains from violence because they fear the judgment of Jesus or they fear bad Karma, it merely matters whether the belief in the story makes them choose non-violent interactions with their fellows over non-violence.
As such, empirical events have little impact on faith in the immediate short-term, because their primary adaptive functions is unconnected to actual material events.
Thirdly, across the world's religions, disasters are interpreted as punishments from the "good" side of the religions instead of being the work of "bad" side, the opposite of what one might expect. But, if you view religions as mechanisms for enhancing cooperations, it makes perfect sense, as the response to a disaster would be an increase in cooperative behaviors as individuals returned to piety.
Based on historical precedent across many cultures, the sudden disappearance of some visible attribute of the divine would rapidly be re-interpreted into some form that maintains social cohesion and cooperation. Likely, there would be a short period of theological fragmentation, but natural selection would rapidly select for the theological explanations that would keep society running.
Fictional Magic Explanation:
All of the above presumes that in the story world, the rings don't actually keep some form of chaos i.e. loss of predictability, separation of cause and effect, from affecting the human world. But if in your story they actually are some kind of supernatural defense, then human society would apparently face a very real upsurge unpredictable and non-casual events.
But likely, they would respond to the situation just like the real world historical societies did because prior to the rise of empiricism in the West staring in the 1500s, real world human societies believed that the world was largely chaotic and unpredictable. Only after Newton created the idea of the Clockmaker god, did the West gradually adopt the idea of nature as a type of predictable mechanism which followed rules that human's could puzzle out.
So, even if the disappearance of the rings did cause real chaos, the theological response would remain the same i.e. reworking the theology so that it continued to foster cooperation and functional social cohesion.
First of all there is no such things as destruction of their beliefs. The disappearance if part of their religion. This is from philosophy field but you always need black to describe white and so on. Without cold you would not know what warm is. You can find this trope in Goethe "Faust"
I am part of that power which eternally wills evil and eternally works good.
Every religion/beliefs need to have "good/bad" to describe itself.
What is important to you is how well the "bad" side is incorporated into the system. If the Motek think that the chaos was and is no more ten the disappearance of the rings would shake the core of their beliefs. So you would have total society destroyed (think Revolution in Russia).
If they think that the war is still going outside the rings then their disappearance would enact the apocalypse scenario (think middle ages with black death or Great Famine of 1315–17).
But to point you to books you asked for I would direct to you to anything about priests in ancient Egypt and their tricks with eclipses. Or to Scientifics explanations of biblical tragedies (did you know that deaths of firstborns were probably caused by the fungus in the stored grains as firstborns were given larger portions?).
Well ignoring the possible religious fracture you have a more important problem, your society is all about structure, in fact if you break out of the order then you are heretic (taking liberties with the term sacrilege you used), now everyone behaves as they should for fear of the gods but more importantly for fear of the reprisal of the mortals around them that will beat them bloody or kick them out of perfect society-chan.
Now the physical representation of these gods are rings that we can see in the sky everyday cementing the notion of order under the heavens, and the fact that you do have place in the universe and that brings you comfort and a sense security. Except that one day there are no rings... So either the gods abandoned you or they went to fight or they died, either way your society now has to deal with the fact that the base of its society is gone...
So they are stranded by their gods and now the backbone of their society is gone. Chaos, confusion and probably violence.
The answer comes from simple theology based on their belief structure.
"in the beginning, the universe was ruled by Chaos, your usual malevolent force of destruction, and life was rough. The Motek gods came to the rescue, sacrificing their own lives by forcing Chaos off the planet and becoming the rings, which act as a shield against the ever-encroaching Chaos."
Irrespective of what made the rings vanish, this will be a sign Chaos has returned and the Motek gods have descended to force Chaos off the planet again. Oh, yes, the gods sacrificed their lives in doing so first time around. The Motek gods have died, but gods have this habit of resurrecting themselves when you least expect it. They were only"sleeping" until they were needed again.
The priests and priestesses will tell their congregations to be vigilant for signs of encroaching Chaos and offer more valuable donations to the priesthood.
Since in societies like this, the priestly caste are almost invariably the astronomers they will be busy making observations about the vanished planetary rings and devising explanations for what happened. Explanations that will be closer to a form of actual science but pure mythology (but not as well formed as science as we know it, is).
Riots, panic, rebellion, and so on, how likely are they? Frankly, not much. The majority of the people will go about their business unperturbed. It will be mainly the priesthood and the ruling classes who have the leisure time to worry about what is essentially a cosmological problem. It's too remote and removed from everyday life to cause much unrest.
Well, actually you solved this for yourself already. Your Motek are set in an ancient Egyptian setting? What happened in Ancient Egypt? The pyramid building era suddenly stopped, but why? Why did they just stop and never continue?
There is much debate around this. Some say finances, some say pyramids are billboards for tombraiders. I disagree. Their tombs were their ticket to the afterlife, their way to 'godhood' of a sorts.
Their belief system in the Pyramid era was the pharaoh advocates to the gods, begs their mercy and blessing for the people of Egypt. Then the Nile didn't flood, the nutrients didn't feed their crops. Famine happened. The people starved, watched their loved ones die one day at a time in a world where they just didn't understand this is a natural occurrence.
So what do the masses believe? Their pharaohs cared more for their tombs than for their people, who --through taxes-- paid for said tomb. So the people become desperate, willing to do anything for food. The pharaoh, of course, won't starve, and the people resent him for it.
One ambitious man rallies the turbulent masses, and is installed as the new pharaoh. His pledge? I will focus on the people, not the tomb.
My point? Fear and desperation, coupled with signs of the gods' anger, would upset the masses. This breeds uncertainty, even paranoia. They need someone to blame, and the leader usually shoulders that burden. Then all you need is one charismatic person that wants change -- intentions are irrelevant. And guess what? It's anyone's game now.
## Religions are built on social networks.
Not belief systems.
Running a social network which is formless, is hard. Most of them put a "form" around it, and that's the set of religious beliefs. The belief systems are the form which the bonds take, but if the form is rendered obsolete, the network will simply take a different form.
Case in point, the start of Star Trek: Into Darkness, here.
I think that trying to find someone to blame would be a rather likely reaction. Much like witches were blamed for all sorts of things, surely someone or some group of people would attract the anger of the masses for doing something wrong - which caused the rings to fall down. "Those pesky people from Village X kept wearing blue pants on tuesdays despite Rule #422 which clearly states that appearing similar to water on weekdays with 'u' in their name offends the gods !"
Once the scapegoats have been punished, most likely killed, the people remaining would feel relieved and united, and start going about business as usual. They know why it happened, they have sorted it out, and the gods will probably be coming back now that they all behave nicely again.
## They would continue to believe anyway
Look at the USA... the science on global climate change is undeniable, so they just ignore it, and vote in a leader who works to supress the evidence.
The OP's people will just explain things away with Alternative Facts and go on believing whatever they want to believe.
• I really like your title - and truly do believe that rationalization would trump (pun fully intentional) rational thought - but the heavy-handed soap boxing has no place here. Also, there is a big difference between scientific evidence for climate change - which most people don't understand and don't see on a daily basis - and the disappearance of a major visible feature in the sky: if our moon suddenly vanished, (the overwhelming majority of) people wouldn't just say, "no it didn't!" just because they didn't understand the statistics being presented. – Ghotir Jan 27 '17 at 18:39
• -1 Yes, well the science of Eugenics was once undeniable as well. In fact, climate change is an eerie recapitulation of Eugenics right down to the social and political demographics. Eugenics was based on the best science of the day. No major scientist questioned it basic premises, the only real debate was whether the government could deal with the problem or not. The only people who opposed the concept did so purely on irrational religious grounds e.g. the Catholic church or because of class e.g. poor whites who were the primary targets of Eugenic sterilization. – TechZen Jan 27 '17 at 19:54
• BTW: If you think Eugenics was dreamed up by Nazis, you're dead wrong. It was nearly 50 years old by the time the Nazis jumped on the bandwagon and they did owing to the concepts popularity. Eugenics was strongly associated with socialism of various stripes if no other reason that only a strong centralized state could impose the degree of control over individual choices necessary to carry out a Eugenics program. – TechZen Jan 27 '17 at 19:58
• And, Eugenics is just one of the stupid ideas dreamed up and broadly accepted by supposed intellectual elites who sneered and mocked at all those backwoods, bible thumping, hicks. Freudian psychology is an excellent example. It was utterly without any scientific or empirical support yet it became the dominate model of human behavior among educated elites for over 70 years. People like you sneered at the hicks for refusing to accept the theory of "Infantile Sexuality" the supposed unquestionable truth that toddles had an innate desire to have sex with their parents. Hicks were right again. – TechZen Jan 27 '17 at 20:04
• @ghotir the fact that the summer has been the hottest on record, several years in a row is about as obvious as the rings disappearing. People will argue about the why of it until they all die. – Innovine Jan 27 '17 at 20:51
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2019-10-22 12:19:49
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http://www.dummies.com/how-to/content/how-to-reduce-fractions-using-prime-factorization.navId-323234.html
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You can use prime factorization to reduce fractions. Start with numbers only and then add variables (letters that represent any real number) to the mix. The beauty of using the prime factorization method is that you can be sure that the fraction’s reduction possibilities are exhausted — that is, you can be certain that you haven’t missed any factors that the numerator and denominator may have in common.
Example: Use these steps to reduce the following fraction.
1. Find the prime factorization of the numerator.
2. Find the prime factorization of the denominator.
165 = 3 × 5 × 11
3. Write the fraction with the prime factorizations in it.
4. Cross out the factors the numerator shares with the denominator to see what’s left — the reduced form.
Example: Reduce the following fraction.
1. Find the prime factorization of the numerator.
2. Find the prime factorization of the denominator.
3. Write the fraction with the prime factorizations.
Look at the prime factorizations. You can see that the numerator and denominator have nothing in common. The fraction can’t be reduced, and so the two numbers are relatively prime. The beauty of using prime factorization is that you can be sure that the fraction’s reduction possibilities are exhausted — you haven’t missed anything. You can leave the fraction in this factored form or go back to the simpler 100/243. It depends on your preference.
Example: Reduce the following fraction that includes variables.
1. Find the prime factorization of the numerator.
2. Find the prime factorization of the denominator.
3. Write the fraction with the prime factorization.
4. Cross out the factors in common.
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2015-07-29 16:13:34
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https://www.chemeurope.com/en/encyclopedia/Generic_scalar_transport_equation.html
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My watch list
my.chemeurope.com
# Generic scalar transport equation
The generic scalar transport equation is a general partial differential equation that describes transport phenomena such as heat transfer, mass transfer, fluid dynamics (momentum transfer), etc. A general form of the equation is
$\frac{\partial \phi}{\partial t } + \nabla \cdot f(t,x,\phi,\nabla\phi) = g(t,x,\phi)$
where f is called the flux, and g is called the source.
All the transfer processes express a certain conservation principle. In this respect, any differential equation addresses a certain quantity as its dependent variable and thus expresses the balance between the phenomena affecting the evolution of this quantity. For example, the temperature of a fluid in a heated pipe is affected by convection due to the solid-fluid interface, and due to the fluid-fluid interaction. Furthermore, temperature is also diffused inside the fluid. For a steady-state problem, with the absence of sources, a differential equation governing the temperature will express a balance between convection and diffusion.
A brief inspection of the equations governing various transport phenomena reveal that all of these equations can be put into a generic form thus allowing a systematic approach for a computer simulation. For example, the conservation equation of a concentration of a substance ci is
$\frac{\partial{\rho c_i}}{\partial t } + \nabla \cdot (\rho \vec u c_i + \vec J) = R_i$
where $\vec u$ denotes the velocity field, $\vec J$ denotes the diffusion flux of the chemical species, and Ri denotes the rate of generation of Ri caused by the chemical reaction.
The x-momentum equation for a Newtonian fluid can be written as
$\frac{\partial{\rho u}}{\partial t} + \nabla \cdot (\rho \vec u u ) =\nabla \cdot (\mu \nabla u ) - \frac {\partial p}{\partial x} + B_x + V_x$
where Bx is the body force in the x-direction and Vx includes the viscous terms that are not expressed by $\nabla \cdot (\mu \nabla u ).$
Upon inspection of the above equations, it can be inferred that all the dependent variables seem to obey a generalized conservation principle. If the dependent variable (scalar or vector) is denoted by φ, the generic differential equation is
$\underbrace{ \frac{\partial{\rho \phi}}{\partial t}}_{\text{Transient term}} + \underbrace{ \nabla \cdot (\rho \vec u \phi )}_{\text{Convection term}} =\underbrace {\nabla \cdot (\Gamma \nabla \phi )}_{\text{Diffusion term}} + \underbrace {S_{\phi}}_{\text{Source term}}$
where Γ is the diffusion coefficient, or diffusivity.
• The transient term, $\frac{\partial{\rho \phi}}{\partial t}$, accounts for the accumulation of φ in the concerned control volume.
• The convection term, $\nabla \cdot (\rho \vec u \phi )$, accounts for the transport of φ due to the existence of the velocity field (note the velocity $\vec u$ multiplying φ).
• The diffusion term, $\nabla \cdot (\Gamma \nabla \phi )$, accounts for the transport of φ due to its gradients.
• The source term, Sφ, accounts for any sources or sinks that either create or destroy φ. Any extra terms that cannot be cast into the convection or diffusion terms are considered as source terms.
The objective of all discretization techniques (finite difference, finite element, finite volume, boundary element, etc.) is to devise a mathematical formulation to transform each of these terms into an algebraic equation. Once applied to all control volumes in a given mesh, we obtain a full linear system of equations that needs to be solved.
## Scalar transport equation in financial mathematics
Some equations that governs the dynamics of financial derivatives in financial markets can be also categorized as generic scalar transport equations. Examples include the Black-Scholes equation.
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2022-12-03 05:40:23
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https://socratic.org/questions/how-do-you-identify-special-products-when-factoring
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# How do you identify special products when factoring?
Jul 21, 2018
You identify special products by their values if its a perfect square or cubes..
#### Explanation:
For examples;
Difference of two squares is: ${x}^{2} - {y}^{2} = \left(x + y\right) \left(x - y\right)$
${\left(x + y\right)}^{2} = {x}^{2} + {y}^{2} + 2 a b$
${\left(x - y\right)}^{2} = {x}^{2} + {y}^{2} - 2 a b$
Note: ${\left(x - y\right)}^{2} \ne {x}^{2} - {y}^{2}$
This Link might help!
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2019-10-17 22:34:41
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https://electronics.stackexchange.com/questions/472545/in-verilog-if-the-always-block-is-executed-sequentially-how-do-non-blocking
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# In Verilog , if the always@ block is executed sequentially , how do non-blocking statements work since they are executed parallely?
I am getting totally confused because contradictory things are given.
In this pdf, it is said that whether the 'always block' will be executed sequentially or parallelly will depend on the assignment used. If nonblocking->parallely else sequentially. But many answers like this
Are Verilog if blocks executed sequentially or concurrently? Says it is always executed sequentially. So I have two doubts
1. Is the 'always' block executed sequentially or parallelly?
2. If sequentially, how do nonblocking statements execute?
• Verilog describes hardware - it's not being "executed in parallel." You are either laying down transistors (or configuring gate arrays) to do all the things all the time. Sequentially just means that it will have a flip-flop at the end of a chain of circuits. Dec 19, 2019 at 22:40
• I think post you linked is referring to how the code parser evaluates your logic, instead of what is being generated in hardware. The always@ block can describe logic sequentially (key word is describe) while synthesizing something that is totally parallel. If it realizes a circuit with flip-flops, then you have sequential logic. Dec 19, 2019 at 22:48
• @AaronD.Marasco Actually the "always @" blocks will get executed in a simulator; sometimes they'll get executed in ways that can't be replicated by a synthesized circuit, in which case (we hope!) the simulation fails. I don't have an example to hand for you, but synthesizable Verilog is a subset of simulatable Verilog. Dec 19, 2019 at 22:52
• Race condition between two always blocks driving the same signal is one example. That's fine in simulation, but the synthesizer will complain bitterly. Dec 20, 2019 at 8:14
Nonblocking assignments simply defer the actual update of the value until all of the statements in the current always block are evaluated. It has the appearance that all of the statements run "concurrently" or "in parallel", but if this was actually the case, it creates an ambiguity: what happens when you assign the same reg two different values in the same always block? If things are truly concurrent, this is a race condition and the new value will be unpredictable. However, the language semantics dictate something else: that the statements must be evaluated sequentially. If you assign the same reg from multiple places in the same always block, the last one takes precedence. Hence, you can consider that the statements are "evaluated" sequentially, but the regs are all updated with new values concurrently.
The synthesizer will convert the HDL code into logic that implements the equivalent functionality. In hardware, things will naturally be evaluated in parallel if there are no data dependencies, but the ordering of the statements would determine the precedence - which value is selected to be loaded into the next register or logic gate.
• Suppose in an always block x<=2; and after that we have x<=3; so after the execution of Always block , x will have value 3 right? Dec 20, 2019 at 9:11
• Yep, that's correct. Dec 20, 2019 at 16:55
• If you have something like c <= x and afterwards c <= {c, &c} will the last statement be equivalent to c <= {x, &x} or not?
– Rhi
Jul 19, 2021 at 8:43
• No, because the value of c will not actually change until the end of the block, so at the end of the block you would see c update to a new value based on the old value of c and having no relation to x. Jul 19, 2021 at 9:19
• @alex.forencich ok thanks, I have posted a question concerning this here electronics.stackexchange.com/questions/576042/…
– Rhi
Jul 19, 2021 at 9:37
You have to separate the software execution semantics in simulation from the hardware semantics in synthesis. Verilog/SystmeVerilog gets used for both. And sometimes the terminology gets reused in different ways, especially the word sequential.
Each always block represents a concurrent process or behavior based on the procedural code you write associated with the block. Certainly styles of code (but not all) can be synthesized into hardware, and that hardware is typically divided into two categories of logic: sequential and combinatorial.
Sequential logic stores state information over time where as combinatorial logic is totally dependent on the immediate inputs to the block. In software, sequential code simply means the is a defined order of execution between statements.
always @(*) begin
a = b + c;
d = a + e;
end
The code above represents combinatorial logic, but the code between the begin/end executes sequentially. If you change the code to
always @(posedge clk) begin
a = b + c;
d = a + e;
end
now you still have sequentially executing statements, but the code now represents a mixture of sequential and combinational logic (only d is sequential). But if you replace the blocking to non-blocking assignments
always @(posedge clk) begin
a <= b + c;
d <= a + e;
end
You still have two assignment statements executing in sequence, but since the update to a is deferred, you now have two sequential logic elements in parallel. Its the same has if you had written the last example in separate always blocks.
always @(posedge clk) begin
a <= b + c;
end
always @(posedge clk) begin
d <= a + e;
end
Your course is being a bit loose on the details.
Something that makes VHDL and Verilog somewhat tricky is that they were originally designed as languages for describing hardware for simulation. They were then later re-used as languages to describe hardware for synthesis.
To understand HDL simulation there are first a couple of basic concepts we must understand.
The first is simulation time, Simulation time is not tied to real-time, it essentially advances when all code paths are waiting for something (either a time delay or a
The second is the concept of time deltas, a time delta represents an infinitesimally small step of simulation time.
Back to always blocks, the contents of an always block in simulation are executed sequentially. A "blocking" assignment takes effect immediately.
A non-blocking assignment reads it's input immediately, but it's result does not take effect until the end of the current time-delta. So, from the programmers perspective, the results of all non-blocking assignments on a given time-delta take effect at the same time.
This is vitally important, because it allows us to describe systems involving multiple "always" blocks in a deterministic manner. The clock triggers all the always blocks to run, the blocks make their calculations, and only once all the blocks have run and we get to the end of the time delta do the results take effect. We can effectively define the state of the system after the clock edge.
As a general rule blocking assignments in clock-triggered always blocks should not be read from anywhere outside the always block in which they are set. Doing so tends to lead quickly to non-deterministic code.
In always blocks that are triggered by all their input signals it tends to matter less, since those blocks will be re-run until all their inputs settle.
Unless you know precisely what you are doing you should avoid getting fancy with always block sensitivity lists, they may work in simulation but they are likely to not work correctly in synthesis.
Synthesis is a different ball-game from simulation, there are many things you can do in Verilog that will work find in simulation but will either cause errors or misbehavior when synthesizing . Essentially the synthesis tool is looking for patterns, clocked always blocks become logic with flip-flops at the output, assignment statements and combinatorial always blocks just become combinatorial logic. If you throw non-standard stuff at it you are likely to get misbehaviour or synthesis failures.
Having said that there is a lot you can do in synthesis too. As long as you keep it within one always block so the order is defined, the compiler will happilly unroll your loops, inline your functions and tasks, and turn your temporary variables into signals, so that the synthesised logic produces the same result as the simulation.
• Verilog/VHDL languages were both designed with synthesis in mind; that was VHDL's initial charter. It's just that it took longer for synthesis tools to appear on the market that could handle it. Dec 20, 2019 at 6:24
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2022-07-02 08:07:38
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https://brilliant.org/discussions/thread/combinatorics-1/
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×
# Combinatorics #1
Given any $$9$$ integers, show that it is possible to choose $$w,x,y,z$$ such that $$w+x-y-z\equiv0$$$$(\text{mod}$$ $$20)$$.
Note by Victor Loh
3 years, 7 months ago
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The condition is the same as:$$w+x\equiv y+z \pmod {20}$$. Notice that if we can find $$w\equiv y, x\equiv z$$, then we are done. Hence it suffices to consider the case where there's at most one residue of $$20$$ such that at most $$3$$ numbers are congruent to it.
In this case, we have at least $$7$$ distinct residues considering each integer in mod 20 . Note that there are at least $${7\choose 2}=21$$ ways to choose $$2$$ of the numbers and then take their sum. Using the $$20$$ mod 20 residues as pigeon holes, there exist a residue $$r$$ with at least two sums i.e $$w+x\equiv y+z\equiv r \pmod {20}$$(we can't have $$w=y$$ because that would imply $$x\equiv z$$ which contradicts having distinct residues) and we are done.
- 3 years, 7 months ago
The easy bash: The 10 possible sets of end digits of the 9 integers are $[1,2,3,4,5,6,7,8,9], [0,1,2,3,4,5,6,7,8], [2,3,4,5,6,7,8,9,0] ,[3,4,5,6,7,8,9,0,1]$ $[4,5,6,7,8,9,0,1,2] , [5,6,7,8,9,1,2,3,4,] ,[6,7,8,9,1,2,3,4,5]$$[7,8,9,1,2,3,4,5,6],[8,9,1,2,3,4,5,6,7] and [9,0,1,2,3,4,5,6,7]$It suffices to show that $$1+9-2-8=0$$ and $$8+0-7-1=0$$ as by Pigeonhole Principle, each of the other 8 sets is just a rearrangement of the first 2. Not very elegant but it works. Since this works for single digit numbers, it works for any other set because each number in that set is basically adding a multiple of 20 to the original 1-digit set. (Not clear, I know but basically, I'm saying that for $$10+19-12-18$$, it works because it is $$1+9-2-8+10+10-10-10$$, or $$1+9+2+8+0$$.)
- 3 years, 7 months ago
one more question, given the series:1,3,5,7,9,11,13,15. now choose 5 digits from here whose sum is equal to 30.(u can take a number twice also)
- 3 years, 6 months ago
$$Odd\times5=Odd$$
- 3 years, 6 months ago
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2018-01-24 01:24:26
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https://www.cs.cornell.edu/courses/cs3110/2019sp/textbook/ads/callbacks.html
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# Callbacks
For a program to benefit from the concurrency provided by asynchronous I/O and promises, there needs to be a way for the program to make use of resolved promises. For example, if a web server is asynchronously reading and serving multiple files to multiple clients, the server needs a way to (i) become aware that a read has completed, and (ii) then do a new asynchronous write with the result of the read. In other words, programs need a mechanism for managing the dependencies among promises.
The mechanism provided in Lwt is named callbacks. A callback is a function that will be run sometime after a promise has been resolved, and it will receive as input the contents of the resolved promise. Think of it like asking your friend to do some work for you: they promise to do it, and to call you back on the phone with the result of the work sometime after they've finished.
## Registering a Callback
Here is a function that prints a string using Lwt's version of the printf function:
let print_the_string str = Lwt_io.printf "The string is: %S\n" str
And here, repeated from the previous section, is our code that returns a promise for a string read from standard input:
let p = read_line stdin
To register the printing function as a callback for that promise, we use the function Lwt.bind, which binds the callback to the promise:
Lwt.bind p print_the_string
Sometime after p is resolved, hence contains a string, the callback function will be run with that string as its input. That causes the string to be printed.
Here's a complete utop transcript as an example of that:
# let print_the_string str = Lwt_io.printf "The string is: %S\n" str;;
val print_the_string : string -> unit Lwt.t = <fun>
# let p = read_line stdin in Lwt.bind p print_the_string;;
- : unit Lwt.t = <abstr>
<type Camels are bae followed by Enter>
# The string is: "Camels are bae"
## Bind
The type of Lwt.bind is important to understand:
'a Lwt.t -> ('a -> 'b Lwt.t) -> 'b Lwt.t
The bind function takes a promise as its first argument. It doesn't matter whether that promise has been resolved yet or not. As its second argument, bind takes a callback function. That callback takes an input which is the same type 'a as the contents of the promise. It's not an accident that they have the same type: the whole idea is to eventually run the callback on the resolved promise, so the type the promise contains needs to be the same as the type the callback expects as input.
After being invoked on a promise and callback, e.g., bind p c, the bind function does one of three things, depending on the state of p:
• If p is already resolved, then c is run immediately on the contents of p. The promise that is returned might or might not be pending, depending on what c does.
• If p is already rejected, then c does not run. The promise that is returned is also rejected, with the same exception as p.
• If p is pending, then bind does not wait for p to be resolved, nor for c to be run. Rather, bind just registers the callback to eventually be run when (or if) the promise is resolved. Therefore the bind function returns a new promise. That promise will become resolved when (or if) the callback completes running, sometime in the future. Its contents will be whatever contents are contained within the promise that the callback itself returns.
(For the first case above: The Lwt source code claims that this behavior might change in a later version: under high load, c might be registered to run later. But as of v4.1.0 that behavior has not yet been activated. So, don't worry about it—this paragraph is just here to future-proof this discussion.)
Let's consider that final case in more detail. We have one promise of type 'a Lwt.t and two promises of type 'b Lwt.t:
• The promise of type 'a Lwt.t, call it promise X, is an input to bind. It was pending when bind was called, and when bind returns.
• The first promise of type 'b Lwt.t, call it promise Y, is created by bind and returned to the user. It is pending at that point.
• The second promise of type 'b Lwt.t, call it promise Z, has not yet been created. It will be created later, when promise X has been resolved, and the callback has been run on the contents of X. The callback then returns promise Z. There is no guarantee about the state of Z; it might well still be pending when returned by the callback.
• When Z is finally resolved, the contents of Y are updated to be the same as the contents of Z.
The reason why bind is designed with this type is so that programmers can set up a sequential chain of callbacks. For example, the following code asynchronously reads one string; then when that string has been read, proceeds to asynchronously read a second string; then prints the concatenation of both strings:
Lwt.bind (read_line stdin) (fun s1 ->
Lwt.bind (read_line stdin) (fun s2 ->
Lwt_io.printf "%s\n" (s1^s2)));;
If you run that in utop, something slightly confusing will happen again: after you press Enter at the end of the first string, Lwt will allow utop to read one character. The problem is that we're mixing Lwt input operations with utop input operations. It would be better to just create a program and run it from the command line.
To do that, put the following code in a file called read2.ml:
open Lwt_io
let p =
Lwt.bind (read_line stdin) (fun s1 ->
Lwt.bind (read_line stdin) (fun s2 ->
Lwt_io.printf "%s\n" (s1^s2))))
let _ = Lwt_main.run p
We've added one new function: Lwt_main.run : 'a Lwt.t -> 'a. It waits for its input promise to be resolved, then returns the contents. Typically this function is called only once in an entire program, near the end of the main file; and the input to it is typically a promise whose resolution indicates that all execution is finished. Without that function, the program above would immediately terminate. (Try it yourself to see.)
Now compile the file, linking the Lwt_unix package, and run the program:
$ocamlbuild -pkg lwt.unix read2.byte$ ./read2.byte
My first string
My second string
My first stringMy second string
## Bind as an Operator
There is another syntax for bind that is used far more frequently than what we have seen so far. The Lwt.Infix module defines an infix operator written >>= that is the same as bind. That is, instead of writing bind p c you write p >>= c. This operator makes it much easier to write code without all the extra parentheses and indentations that our previous example had:
open Lwt_io
open Lwt.Infix
let p =
read_line stdin >>= fun s1 ->
read_line stdin >>= fun s2 ->
Lwt_io.printf "%s\n" (s1^s2)
let _ = Lwt_main.run p
The way to visually parse the definition of p is to look at each line as computing some promised value. The first line, read_line stdin >>= fun s1 -> means that a promise is created, resolved, and its contents extracted under the name s1. The second line means the same, except that its contents are named s2. The third line creates a final promise whose contents are eventually extracted by Lst_main.run, at which point the program may terminate.
The >>= operator is perhaps most famous from the functional language Haskell, which uses it extensively for monads. We'll cover monads as our next major topic.
## Bind as Let Syntax
There is a syntax extension for OCaml that makes using bind even simpler than the infix operator >>=. To install the syntax extension, run the following command:
\$ opam install lwt_ppx
(You might need to opam update followed by opam upgrade first.)
With that extension, you can use a specialized let expression written let%lwt x = e1 in e2, which is equivalent to bind e1 (fun x -> e2) or e1 >>= fun x -> e2. We can rewrite our running example as follows:
(* compile with:
ocamlbuild -use-ocamlfind -pkgs lwt.unix,lwt_ppx -tag thread read2.byte *)
open Lwt_io
let p =
let%lwt s1 = read_line stdin in
let%lwt s2 = read_line stdin in
Lwt_io.printf "%s\n" (s1^s2)
let _ = Lwt_main.run p
Now the code looks pretty much exactly like what its equivalent synchronous version would be. But don't be fooled: all the asynchronous I/O, the promises, and the callbacks are still there. Thus, the evaluation of p first registers a callback with a promise, then moves on to the the evaluation of Lwt_main.run without waiting for the first string to finish being read. To prove that to yourself, run the following code:
open Lwt_io
let p =
let%lwt s1 = read_line stdin in
let%lwt s2 = read_line stdin in
Lwt_io.printf "%s\n" (s1^s2)
let _ = Lwt_io.printf "Got here first\n"
let _ = Lwt_main.run p
You'll see that "Got here first" prints before you get a chance to enter any input.
## Concurrent Composition
The Lwt.bind function provides a way to sequentially compose callbacks: first one callback is run, then another, then another, and so forth. There are other functions in the library for composition of many callbacks as a set. For example,
• Lwt.join : unit Lwt.t list -> unit Lwt.t enables waiting upon multiple promises. Lwt.join ps returns a promise that is pending until all the promises in ps become resolved. You might register a callback on the return promise from the join to take care of some computation that needs all of a set of promises to be finished.
• Lwt.pick : 'a Lwt.t list -> 'a Lwt.t also enables waiting upon multiple promises, but Lwt.pick ps returns a promise that is pending until at least one promise in ps becomes resolved. You might register a callback on the return promise from the pick to take care of some computation that needs just one of a set of promises to be finished, but doesn't care which one.
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2019-08-19 06:14:17
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http://icpc.njust.edu.cn/Problem/Local/1387/
|
# Compromise
Time Limit: 1000 ms
Memory Limit: 65535 ms
## Description
In a few months the European Currency Union will become a reality. However, to join the club, the Maastricht criteria must be fulfilled, and this is not a trivial task for the countries (maybe except for Luxembourg). To enforce that Germany will fulfill the criteria, our government has so many wonderful options (raise taxes, sell stocks, revalue the gold reserves,...) that it is really hard to choose what to do.
Therefore the German government requires a program for the following task:
Two politicians each enter their proposal of what to do. The computer then outputs the longest common subsequence of words that occurs in both proposals. As you can see, this is a totally fair compromise (after all, a common sequence of words is something what both people have in mind).
Your country needs this program, so your job is to write it for us.
## Input
The input file will contain several test cases. Each test case consists of two texts. Each text is given as a sequence of lower-case words, separated by whitespace, but with no punctuation. Words will be less than 30 characters long. Both texts will contain less than 100 words and will be terminated by a line containing a single '#'. Input is terminated by end of file.
## Output
For each test case, print the longest common subsequence of words occuring in the two texts. If there is more than one such sequence, any one is acceptable. Separate the words by one blank. After the last word, output a newline character.
## Sample Input
die einkommen der landwirte
sind fuer die abgeordneten ein buch mit sieben siegeln
um dem abzuhelfen
muessen dringend alle subventionsgesetze verbessert werden
#
die steuern auf vermoegen und einkommen
sollten nach meinung der abgeordneten
nachdruecklich erhoben werden
dazu muessen die kontrollbefugnisse der finanzbehoerden
dringend verbessert werden
#
## Sample Output
die einkommen der abgeordneten muessen dringend verbessert werden
Ulm Local
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2019-08-26 05:04:46
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|
https://17calculus.com/differential-equations/substitution/
|
First Order Second Order Laplace Transforms Additional Topics Applications, Practice
Separation of Variables
Linear
Integrating Factors (Linear)
Substitution
Exact Equations
Integrating Factors (Exact)
Linear
Constant Coefficients
Substitution
Reduction of Order
Undetermined Coefficients
Variation of Parameters
Polynomial Coefficients
Cauchy-Euler Equations
Chebyshev Equations
Laplace Transforms
Unit Step Function
Unit Impulse Function
Square Wave
Shifting Theorems
Solve Initial Value Problems
Classify Differential Equations
Fourier Series
Slope Fields
Wronskian
Existence and Uniqueness
Boundary Value Problems
Euler's Method
Inhomogeneous ODE's
Resonance
Partial Differential Equations
Linear Systems
Exponential Growth/Decay
Population Dynamics
Projectile Motion
Chemical Concentration
Fluids (Mixing)
Practice Problems
Practice Exam List
Exam A1
Exam A3
Exam B2
You CAN Ace Differential Equations
17calculus > differential equations > substitution
### Differential Equations Alpha List
Boundary Value Problems Cauchy-Euler Equations Chebyshev Equations Chemical Concentration Classify Differential Equations Constant Coefficients Euler's Method Exact Equations Existence and Uniqueness Exponential Growth/Decay First Order, Linear Fluids (Mixing) Fourier Series Inhomogeneous ODE's Integrating Factors (Exact) Integrating Factors (Linear) Laplace Transforms Linear Systems Partial Differential Equations Polynomial Coefficients Population Dynamics Projectile Motion Reduction of Order Resonance Second Order, Linear Separation of Variables Shifting Theorems Slope Fields Solve Initial Value Problems Square Wave Substitution Undetermined Coefficients Unit Impulse Function Unit Step Function Variation of Parameters Wronskian
### Tools
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external links you may find helpful related topics on other pages precalculus substitution integration by substitution integration by trig substitution substitution youtube playlist Wikibooks - Substitution Pauls Online Math Notes - Differential Equations Substitution Wikipedia - Bernoulli Differential Equation
Substitution Technique for Differential Equations
Alternate Name For Substitution - Change of Variables
Sometimes we can solve a differential equation by using substitution and changing the variables. This changes the equation into one where we can use a technique we learned previously. There are several different kinds of substitutions that can be done. These are listed below with links to the appropriate discussion.
Given in the Problem Statement
This, of course, is the easiest kind of substitution you can have. You don't have to analyze or classify the differential equation and then make a determination of what type of substitution will help transform the equation into one that you can solve. The thing to remember here is to make sure and take the derivative of the substitution and substitute for the differentials based on what you are given. For example, if your original variable is x and the new one is t, you can't just say that $$dx = dt$$. You need to calculate $$dt$$ based on your equation. ( You probably remember this from integration by substitution. The same rule applies here. )
Here is a video showing this technique with an example and lots of detail. This is great place to start to understand what is involved with the technique of substitution.
Dr Chris Tisdell - substitution technique
Okay, after watching that video, you should have a clue what substitution is about and how to accomplish it. The trick now is to learn how to choose a substitution on your own, based on what the differential equation looks like. The next video explains the next three techniques, scaling, Bernoullis equation and homogeneous ODEs. But before viewing that video, let's give a quick overview of these three techniques.
Basic $$v=y'$$
In the special case when you have a second order equation with the dependent variable missing, you can use the substitution $$v=y'$$ to reduce it to a first order equation, find $$v$$ and then integrate to get $$y$$. This technique can be used to solve these two practice problems.
$$y''+y'=t$$ $$ty''-2y'=12t^2$$
Scaling
Sometimes we may just want to scale the equation to make it easier to work with or make it dimensionless. In order to do that, we use these substitutions.
$$x_1 = x/a$$ $$y_1 = y/b$$ where x and y are the old variables $$x_1$$ and $$y_1$$ are the new variables, and a and b are constants
Bernoulli Equation
For equations of the type $$y' = p(x)y + q(x)y^n$$, called a Bernoulli equation, we can use the direct substitution $$v = y^{1-n}$$, which will turn the equation into a linear equation.
[ Note: This technique uses integrating factors in order to solve the resulting linear equation. ]
Homogeneous ODEs
These first order, linear differential equations can be written in the form, $$y' = f(y/x)$$, which should make it obvious that the substitution we use is $$z=y/x$$. This is the most common form of substitution taught in first year differential equations.
Now that you have an idea of these three types of substitution, watch this in-depth video to get some examples and detailed explanation on all three topics. If you have not had integrating factors yet, don't worry. You don't need it to understand this video.
MIT OCW - substitution
Cauchy-Euler Equation
When you have an equation of the form $$\displaystyle{ x^2\frac{d^2y}{dx^2} + ax\frac{dy}{dx} + by = 0, ~~~ x > 0 }$$, where a and b are constants, you have an Cauchy-Euler equation. One substitution that works here is to let $$t = \ln(x)$$. This substitution changes the differential equation into a second order equation with constant coefficients. We discuss this in more detail on a separate page.
As you can tell from the discussion above, there are many types of substitution problems, each with its own technique. We have touched on only a few here. Go through your textbook or search the internet and see if you can find others. If you need a good differential equations textbook, you can find several options at the 17calculus bookstore.
### Search 17Calculus
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given (2)
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Practice Problems
Instructions - - Unless otherwise instructed, solve these differential equations using substitution. Give your answers in exact form.
Level A - Basic
Practice A01
$$\displaystyle{\frac{dy}{dx}=\frac{x^2+y^2}{2x^2}}$$
solution
Practice A02
$$\displaystyle{x\frac{dy}{dx}+y=xy^2}$$; $$y=1/v$$
solution
Practice A03
$$\displaystyle{y'=x+y}$$; $$u=x+y$$
solution
Practice A04
$$\displaystyle{\frac{dy}{dx}=\frac{x+y}{x}}$$
solution
Practice A05
$$y''+y'=t$$
solution
Practice A06
$$ty''-2y'=12t^2$$; $$t > 0$$
solution
Level B - Intermediate
Practice B01
$$\displaystyle{\frac{dy}{dx}=\frac{y^2-x^2}{xy}}$$
solution
Practice B02
$$\displaystyle{\frac{dy}{dx}=\frac{y^3+y^2x+yx^2}{yx^2}}$$
solution
Practice B03
$$\displaystyle{\frac{dy}{dx}=\frac{y^4+yx^3}{x^4}}$$
solution
Practice B04
$$\displaystyle{\frac{dy}{dx}=\frac{x^2+3y^2}{2xy}}$$
solution
Practice C01
$$\displaystyle{\frac{dy}{dx}=\frac{y^3+2y^2x-yx^2}{yx^2+x^3}}$$
solution
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2017-09-22 09:56:10
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https://www.asterics2020.eu/dokuwiki/doku.php?id=open:wp4:wp4techforum5:hackathon&rev=1551689514&do=diff
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# ASTERICS Wiki pages
### Site Tools
open:wp4:wp4techforum5:hackathon
# Differences
This shows you the differences between two versions of the page.
open:wp4:wp4techforum5:hackathon [2019/02/28 09:26]
nebot
open:wp4:wp4techforum5:hackathon [2019/03/04 09:51] (current)
morten
Line 11: Line 11:
I ) ObsCore and other VO standards in the context of EST and solar data I ) ObsCore and other VO standards in the context of EST and solar data
-Participants Morten Frantz, Marco Guenter, Thomas Hederer, François Bonnarel +Participants Morten Franz, Thomas Hederer, Carl Schaffer, François Bonnarel
Discussion was about how Solar data can be described and discovered using an ObsCOre/EPNTAP strategy. Discussion was about how Solar data can be described and discovered using an ObsCOre/EPNTAP strategy.
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2019-11-14 08:29:24
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https://www.physicsforums.com/threads/verbal-problem.530788/
|
# Verbal Problem
1. Sep 16, 2011
### athamz
1. The problem statement, all variables and given/known data
A bag containing a mixture of 6 mangoes and 12 guavas sold for $234. A smaller bag containing 2 mangoes and 4 guavas sold for$77. An alert shopperasked the salesclerk if it was better to purchase the larger bag. The clerk was not sure, but said that it really made no difference because the price of each package was based on the same unit price for each kind of fruit. Why was the clerk wrong?
2. Relevant equations
3. The attempt at a solution
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
2. Sep 16, 2011
### Hootenanny
Staff Emeritus
You appear to have forgotten something:
3. Sep 16, 2011
### athamz
I am sorry, but I don't know how and when to start, could you help me?
4. Sep 16, 2011
### Hootenanny
Staff Emeritus
What is the ratio between the pieces of fruit and prices in each case?
5. Sep 16, 2011
### Ray Vickson
You have two equations in the two unknowns m = price per mango and g = price per guava. What happens when you start to solve them?
RGV
6. Sep 16, 2011
If "$" means USD, that is some VERY expensive fruit. 7. Sep 16, 2011 ### HallsofIvy Staff Emeritus That was my thought! 8. Sep 16, 2011 ### athamz I have this Equation using x and y variables. x for price per mango and y for price per mango. so the equations are 6x + 12y = 234 and 2x + 4y = 77.. But I did not get the value for the x and y using that two equations... It says in the problem that the sales clerk was wrong.. I think there's something wrong with the equations.. Help me please... 9. Sep 16, 2011 ### ArcanaNoir How many small bags of fruit equal one big bag of fruit in number of fruit? (ignore the cost of the bags) once you know that, you should be able to tell which bag is a better deal. 10. Sep 16, 2011 ### athamz But How can I do that? can you give me the first step? 11. Sep 16, 2011 ### symbolipoint athamz wrote problem description: Notice the ratio of mango to guava is the same for each bag. This ratio is 1 mango to 2 guava. You are then really interested in price as number of fruit for each dollar of cost. This becomes really just a one-step problem in two parts; large bag part, and small bag part. How many pieces of fruit in the large bag? What is ratio of number of fruit to price of large bag? How many pieces of fruit in the small bag? What is the ratio of number of fruit to price of small bag? 12. Sep 16, 2011 ### Mark44 ### Staff: Mentor Don't you notice something about these two equations? If two mangoes and four guavas cost$77, how much would you expect to pay for four mangoes and eight guavas?
No, your equations are fine, except how you defined y - it should be the price per guava.
13. Sep 16, 2011
### athamz
Can you give me the equation? I don't know how to form equation...
14. Sep 16, 2011
### Staff: Mentor
We are NOT here to do your work for you. We are happy to help you and steer you in the right direction, but you need to do most of the work. If you go back and reread what people have written here, you should be able to do this problem.
15. Sep 16, 2011
### quietrain
if 2 nuggets cost $10, and 4 nuggets cost$18, which is the better deal?
assuming you like eating that is..
16. Sep 17, 2011
### HallsofIvy
Staff Emeritus
Reread your original problem. "The clerk was not sure, but said that it really made no difference because the price of each package was based on the same unit price for each kind of fruit. Why was the clerk wrong?"
That does NOT ask you to find the price of each fruit in each package- only to say why it was not the same for the two packages. That is, x and y cannot be the same in the two equations. You said,
"I did not get the value for the x and y using that two equations...
I think there's something wrong with the equations.."
Yes, that's the whole point of the problem!
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2017-11-23 06:31:04
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https://home.cern/news/news/cern/quantum-field-theorist-wins-fundamental-physics-prize
|
Voir en
français
# Quantum field theorist wins Fundamental Physics Prize
The $3 million Fundamental Physics Prize was awarded last night to theorist Alexander Polyakov of Princeton University | Alexander Polyakov, laureate of 2013 Physics Frontiers Prize, delivers a speech during the Fundamental Physics Prize Foundation Inaugural Prize Ceremony in Geneva, Switzerland (Image: Harold Cunningham/Getty Images) The$3 million Fundamental Physics Prize was awarded last night to theorist Alexander Polyakov of Princeton University, for his many discoveries in field theory and string theory.
Polyakov was chosen from among five laureates of the Physics Frontiers Prize, which recognizes achievements that push forward the boundaries of physics. He warmly thanked Princeton University and his former place of work, the Landau Institute in Moscow, for "tolerating" what he called the eccentric way in which he does physics.
Polyakov's discoveries in theoretical physics include the conformal bootstrap, magnetic monopoles, instantons, confinement and de-confinement, the quantization of strings in non-critical dimensions, gauge/string duality and many others.
At a ceremony in Geneva, Switzerland, last night, Polyakov said he was "bewildered and overwhelmed" to receive the prize.
Russian technology-investor Yuri Milner launched the $27 million Fundamental Physics Prize Foundation in July last year to recognize advances in physics. The foundation awards$3 million every year to researchers in fundamental physics, who are then invited to select recipients of future prizes.
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2020-10-22 15:25:31
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https://www.acmicpc.net/problem/7334
|
시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 1 0 0 0.000%
## 문제
It's now 3002 and the Godfather Unlucky Luchiano is planning a rubbery from the Rectilinia museum. The problem is that the walls of the museum are impenetrable and the doors are guarded so his men cannot enter the museum from its doors. He is lucky that the museum has no roofs and one can enter the museum from the above. So he decides to use a device from thousands of years ago; a catapult! Using this, his men can fly and fall in some place in the museum without being caught by guards.
But another problem still exists which is a high-tech laser gun that guards the museum. The laser gun is designed based on a very recent discovery that it is possible to guide the laser beam not on a straight line, but on a rectilinear path. The fact that the beam travels the shortest (possible) distance from the emission point to a target still remains. The problem is that if one land somewhere in the museum that is reachable by the laser beams, he will be immediately destroyed. Again godfather is lucky, since in the museum, there are some walls and other obstacles through which the beam cannot pass and if his men can land in the shadows of that walls, they are safe in the way that they are not destroyed by the gun right after landing and they can use their special device to disable the laser gun. As the catapult is not a very precise device, godfather wants to know the probability of landing in shadows, so he has to compute the total area of shadowy regions of the museum.
Given the layout of the museum, you have to write a program to compute the total area of the shadowy regions. Yes! This time you really HAVE TO!
As you study the layout of the museum from the top view, you find that the museum can be considered as a rectangle with some obstacles in it. The obstacles are simple polygons with sides parallel to the rectangle sides. Interior of obstacles do not overlap. The laser gun is located in the upper-right corner of the museum. A laser beam is composed of a number of line segments; each is either horizontal or vertical. When the gun chooses its target, it intelligently determines a possible path to the target and fires. A possible path has the following characteristics:
• It consists of only horizontal and vertical segments.
• It never crosses an obstacle but in some parts may be tangent to obstacle sides. It can never be tangent to two obstacle sides at one point.
• In the travel from the gun to the target, the beam never moves from left to right or from bottom to top (directions are relative to view of the museum from the above).
The problem is to compute the total area of the shadowy regions in the museum (not belonging to the interior of the obstacles), where the laser gun cannot shoot any point inside those regions. In the above figure, the point marked by (x) is in a shadowy region (see sample input).
## 입력
The input file contains several test cases. The first line contains a single integer t (between 1 and 10), which is the number of test cases. Rest of the input file contains t test cases. The first line of each test case contains 2 positive integers, which are the length and the width of the rectangle respectively. The second line contains a single integer n, which is the number of obstacles in the museum (between 0 and 50). After it, there are n lines, which contain the obstacle data. Each obstacle data is in a single line, which begins with an integer m, which is the number of vertices of the obstacle (between 4 and 50), followed by 2m numbers, which are the x, and y coordinates of the vertices listed in clockwise order. Every coordinate in the input is a positive integer less than 1,000,000. Upper-left corner of the rectangle is the coordinate origin.
## 출력
The output file must contain exactly t lines. Each line contains a single number, which is the total area of the safe regions in the test case. The output for each test case is guaranteed to fit in a 32-bit integer.
## 예제 입력
1
12 8
3
8 5 1 11 1 11 5 7 5 7 4 9 4 9 2 5 2
4 0 3 3 3 3 4 0 4
4 1 4 2 4 2 6 1 6
## 예제 출력
12
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2017-09-19 15:38:39
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https://quant.stackexchange.com/questions/25907/choice-between-2-investments-that-cost-the-same-but-offer-different-interest-and
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# Choice between 2 investments that cost the same but offer different interest and face value [closed]
Assume, you have a choice between two investments that both cost \$1000 each, however investment A pays \$20 a year and \$950 at the end of year 5 but investment B pays \$10 a year and \\$1000 at the end of the 5 years. Which investment should I choose based on it offering a better return?
## closed as off-topic by Bob Jansen♦May 9 '16 at 15:57
This question appears to be off-topic. The users who voted to close gave this specific reason:
• "Basic financial questions are off-topic as they are assumed to be common knowledge for those studying or working in the field of quantitative finance." – Bob Jansen
If this question can be reworded to fit the rules in the help center, please edit the question.
• zhqiat makes a good suggestion but this type of question is not appropriate for this site, please see the faq. – Bob Jansen May 9 '16 at 15:58
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2019-10-14 03:31:19
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https://byjus.com/question-answer/abcd-is-a-parallelogram-if-the-coordinates-of-a-b-c-are-2-1-3/
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Question
# ABCD is a parallelogram. If the coordinates of A, B, C are (−2, −1), (3, 0) and (1, −2) respectively, find the coordinates of D.
Open in App
Solution
## Let the coordinates of $D$ is $\left(x,y\right)$. Since, $ABCD$ is a parallelogram. ∴ $AB=DC$ We have, $\stackrel{\to }{AB}=\stackrel{\to }{DC}\phantom{\rule{0ex}{0ex}}⇒3\stackrel{⏜}{i}-\left(-2\stackrel{⏜}{i}-\stackrel{⏜}{j}\right)=\left(\stackrel{⏜}{i}-2\stackrel{⏜}{j}\right)-\left(x\stackrel{⏜}{i}+y\stackrel{⏜}{j}\right)\phantom{\rule{0ex}{0ex}}⇒5\stackrel{⏜}{i}+\stackrel{⏜}{j}=\stackrel{⏜}{i}\left(1-x\right)+\stackrel{⏜}{j}\left(-2-y\right)\phantom{\rule{0ex}{0ex}}⇒1-x=5\mathrm{and}1=-2-y\phantom{\rule{0ex}{0ex}}⇒x=-4\mathrm{and}y=-3$ Hence, the coordinates of $D$ is $\left(-4,-3\right)$
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2023-03-29 13:02:14
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https://hal.inria.fr/hal-01579063
|
# Sequential Dirichlet Process Mixtures of Multivariate Skew t-distributions for Model-based Clustering of Flow Cytometry Data
2 SISTM - Statistics In System biology and Translational Medicine
Epidémiologie et Biostatistique [Bordeaux], Inria Bordeaux - Sud-Ouest
Abstract : Flow cytometry is a high-throughput technology used to quantify multiple surface and intracellular markers at the level of a single cell. This enables to identify cell sub-types, and to determine their relative proportions. Improvements of this technology allow to describe millions of individual cells from a blood sample using multiple markers. This results in high-dimensional datasets, whose manual analysis is highly time-consuming and poorly reproducible. While several methods have been developed to perform automatic recognition of cell populations, most of them treat and analyze each sample independently. However, in practice, individual samples are rarely independent (e.g. longitudinal studies). Here, we propose to use a Bayesian nonparametric approach with Dirichlet process mixture (DPM) of multivariate skew $t$-distributions to perform model based clustering of flow-cytometry data. DPM models directly estimate the number of cell populations from the data, avoiding model selection issues, and skew $t$-distributions provides robustness to outliers and non-elliptical shape of cell populations. To accommodate repeated measurements, we propose a sequential strategy relying on a parametric approximation of the posterior. We illustrate the good performance of our method on simulated data, on an experimental benchmark dataset, and on new longitudinal data from the DALIA-1 trial which evaluates a therapeutic vaccine against HIV. On the benchmark dataset, the sequential strategy outperforms all other methods evaluated, and similarly, leads to improved performance on the DALIA-1 data. We have made the method available for the community in the R package NPflow.
Keywords :
Document type :
Journal articles
Cited literature [60 references]
https://hal.inria.fr/hal-01579063
Contributor : Boris Hejblum <>
Submitted on : Saturday, October 6, 2018 - 10:44:09 AM
Last modification on : Monday, December 30, 2019 - 2:19:24 PM
### File
NPflowAOAS_final.pdf
Files produced by the author(s)
### Citation
Boris P. Hejblum, Chariff Alkhassim, Raphael Gottardo, François Caron, Rodolphe Thiébaut. Sequential Dirichlet Process Mixtures of Multivariate Skew t-distributions for Model-based Clustering of Flow Cytometry Data. Annals of Applied Statistics, Institute of Mathematical Statistics, 2019, 13 (1), pp.638-660. ⟨10.1214/18-AOAS1209⟩. ⟨hal-01579063⟩
Record views
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2020-01-20 21:41:05
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https://math.stackexchange.com/questions/4165697/arctan-fracx1x-1-to-power-series/4165707
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# $\arctan(\frac{x+1}{x-1})$ to power series
EDIT: I just realize that I should start with the derivative of $$\arctan(\frac{x+1}{x-1})$$ , and keep going from there.
So $$(\arctan(\frac{x+1}{x-1}))'=\frac{1}{1+x^2}$$, does that mean this is the same series as $$\arctan(x)$$?
--
I want to find an expression for $$\arctan(\frac{x+1}{x-1})$$ as a power series, with $$x_0=0$$, for every $$x \ne 1$$.
My initial thought was to use the known $$\arctan(x)=\sum_{n=0}^\infty \frac{(-1)^n x^{2n+1}}{2n+1}$$, but I don't know how to keep going if I replace $$x$$ with $$\frac{x+1}{x-1}$$.
Thanks a lot!
• Really, start with the derivative and simplify it. Jun 7 at 8:28
• Thank you @IvanNeretin, so it has the same derivative as $\arctan(x)$, is that mean that they share the same series? Jun 7 at 8:30
• Plug 0 in both $\arctan(x)$ and $\arctan(\frac{x+1}{x-1})$. You should be able to see the difference. Jun 7 at 8:38
• @CalculusLover Do not forget that there could be a non-zero constant of integration when returning to the original function.
– Gary
Jun 7 at 8:41
• @Gary, yes I just figured out that is $\frac{\pi}{4}$. Thanks! Jun 7 at 8:44
Use the identity $$\arctan(\frac{x+1}{x-1}) = - \arctan(\frac{x+1}{1 - x}) = - (\pi/4 + \arctan(x))$$
• Wow that is a cool answer! Jun 7 at 8:45
Let $$f\left(x\right)=\arctan\left(\frac{1+x}{1-x}\right),\;\;\forall |x|<1$$ .
It can be easily showed that: $$f'\left(x\right)=\frac{1}{1+x^{2}}=\sum_{n=0}^{\infty}\left(-1\right)^{n}x^{2n}$$ Integrating both sides yields that $$\exists C\in \mathbb R$$ such that: $$\arctan\left(\frac{1+x}{1-x}\right)+C=\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}x^{2n+1}}{2n+1}$$ Check for $$f(0)$$ to conclude $$C$$ and you're done.
• Great, exactly what I ended up with. Thanks again! Jun 7 at 8:45
• Always a pleasure ! :) Jun 7 at 8:49
Since $$\frac{d}{dx}\arctan\left(\frac{x+1}{x-1}\right)=-\frac{1}{1+x^2},$$ you can express the RHS as a power series, and then integrate the result to get the desired series for your original function $$\arctan\left(\frac{x+1}{x-1}\right)$$.
• Thank you for that, the derivative has a $+$ in this case. Jun 7 at 8:46
• I'd double check that if I were you Jun 7 at 8:48
• check it again my friend :) Jun 7 at 9:30
• wolframalpha.com/input/… Jun 7 at 9:32
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2021-10-25 07:10:22
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https://www.askiitians.com/forums/Modern-Physics/prove-that-beta-equal-2-alpha-and-prove-that-gamma_256425.htm
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# Prove that beta equal 2 alpha and prove that gamma equal 3 alpha.
Arun
25757 Points
3 years ago
Denote by
α : the coefficient of linear expansion
β : the coefficient of surface expansion
γ : the coefficient of volumetric expansion
Then a length increases as
L → L ( 1 + α ΔT)
But this means that for isotropic (same in every direction) expansion a surface (length x length) increases as
A → A ( 1 + α ΔT)( 1 + α ΔT) ≈ A (1 +2 α ΔT)
where we have neglected the (usually very small) square term (α ΔT)² .
Comparing with the (definition of β) expression
A → ( 1 + βΔT) , we see the relation
β = 2α .
Likewise
V → V ( 1 + γ ΔT) from the definition of volumetric expansion coefficient.
But also we can approximate (volume = length x length x length)
V → V ( 1 + α ΔT)³ ≈ V ( 1 + 3 α ΔT) , neglecting higher powers of α ΔT.
Hence
γ = 3 α
Hope it helps
Sai Soumya
99 Points
3 years ago
You can find the answer in class 11 NCERT book in the chapter Kinetic Theory of Gases.
It has been briefly explained
Otherwise you can refer to any reference book
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2023-03-27 00:02:47
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https://gmatclub.com/forum/if-x-3-is-x-1-x-233797.html
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# If x < 3, is (x + 1)/(x - 3) > 1/3?
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If x < 3, is $$\frac{x + 1}{x - 3}$$ > 1/3?
(1) x < 2
(2) x > -1
*Kudos for all correct solutions
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Re: If x < 3, is (x + 1)/(x - 3) > 1/3? [#permalink]
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Updated on: 10 Feb 2017, 10:23
2
(x + 1)/(x - 3) - 1/3 > 0?
2(x + 3)/3(x -3) > 0? --> We have to find out whether the expression (x + 3)/(x - 3) is positive.
St1: x < 2 --> The expression can be positive, negative or zero.
Insufficient.
St2: x > -1 --> -1 < x < 3 --> Numerator is always positive and denominator is always negative. So the expression is negative.
Sufficient.
Originally posted by Vyshak on 10 Feb 2017, 09:58.
Last edited by Vyshak on 10 Feb 2017, 10:23, edited 1 time in total.
Typo
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Re: If x < 3, is (x + 1)/(x - 3) > 1/3? [#permalink]
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10 Feb 2017, 10:08
Top Contributor
Vyshak wrote:
(x + 1)/(x - 1) - 1/3 > 0?
2(x + 3)/3(x -3) > 0? --> We have to find out whether the expression (x + 3)/(x - 3) is positive.
St1: x < 2 --> The expression can be positive, negative or zero.
Insufficient.
St2: x > -1 --> -1 < x < 3 --> Numerator is always positive and denominator is always negative. So the expression is negative.
Sufficient.
I think you may have incorrectly transcribed the question.
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Marshall & McDonough Moderator
Joined: 13 Apr 2015
Posts: 1675
Location: India
Re: If x < 3, is (x + 1)/(x - 3) > 1/3? [#permalink]
### Show Tags
10 Feb 2017, 10:24
GMATPrepNow wrote:
Vyshak wrote:
(x + 1)/(x - 1) - 1/3 > 0?
2(x + 3)/3(x -3) > 0? --> We have to find out whether the expression (x + 3)/(x - 3) is positive.
St1: x < 2 --> The expression can be positive, negative or zero.
Insufficient.
St2: x > -1 --> -1 < x < 3 --> Numerator is always positive and denominator is always negative. So the expression is negative.
Sufficient.
I think you may have incorrectly transcribed the question.
Thanks. I have corrected it now. But the steps seem to be fine.
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Re: If x < 3, is (x + 1)/(x - 3) > 1/3? [#permalink]
### Show Tags
10 Feb 2017, 11:54
Top Contributor
3
GMATPrepNow wrote:
If x < 3, is $$\frac{x + 1}{x - 3}$$ > 1/3?
(1) x < 2
(2) x > -1
Given: x < 3
Target question: Is (x + 1)/(x - 3) > 1/3?
This is a good candidate for rephrasing the target question.
Aside: See below for a video with tips on rephrasing the target question
Since x < 3, we know that (x - 3) will always be NEGATIVE.
So, let's take (x + 1)/(x - 3) > 1/3, and multiply both sides by (x - 3)
We get: x + 1 < (1/3)(x - 3) [ASIDE: since we multiplied both sides by a NEGATIVE value, we REVERSED the inequality sign]
Now take x + 1 < (1/3)(x - 3) and multiply both sides by 3 to get: 3(x + 1) < x - 3
Expand to get: 3x + 3 < x - 3
Subtract x from both sides: 2x + 3 < -3
Subtract 3 from both sides: 2x < -6
Divide both sides by 2 to get: x < -3
This equivalent inequality is much easier to work with. So, ....
REPHRASED target question: Is x < -3?
Statement 1: x < 2
There are several values of x that satisfy statement 1. Here are two:
Case a: x = -7, in which case x < -3
Case b: x = 0, in which case x > -3
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x > -1
If x is greater than -1, then we can be 100% certain that x IS NOT less than -3
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT
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If x < 3, is (x + 1)/(x - 3) > 1/3? [#permalink]
### Show Tags
22 Jun 2017, 02:20
Step 1-
(x-3)+4
X-3
gives
1+4/(x-3)>1/3
(2/(x-3))>-1/3
Now, option b , since x>-1 & <3,LHS can never be greater than -1/3
So B is sufficient
VP
Joined: 24 Nov 2016
Posts: 1200
Location: United States
If x < 3, is (x + 1)/(x - 3) > 1/3? [#permalink]
### Show Tags
19 Nov 2019, 04:25
GMATPrepNow wrote:
If x < 3, is $$\frac{x + 1}{x - 3}$$ > 1/3?
(1) x < 2
(2) x > -1
$$\frac{x+1}{x-3}>1/3…\frac{(x+1)3-(x-3)1}{3(x-3)}>0…\frac{3x+3-x+3}{3x-9}>0…\frac{2(x+3)}{3(x-3)}>0$$
$$\frac{2(x+3)}{3(x-3)}>0…\frac{(x+3)}{x-3}>0…true:x<-3$$
$$(ie).x=-7:\frac{2(-7+3)}{3(-7-3)}>0…\frac{2(-4)}{3(-10)}>0…\frac{-8}{-30}>0$$
(1) x < 2 insufic
(2) x > -1 sufic
Ans (B)
If x < 3, is (x + 1)/(x - 3) > 1/3? [#permalink] 19 Nov 2019, 04:25
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2020-02-17 21:07:21
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https://mathalino.com/forum/calculus/basic-calculus#comment-13035
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# Basic Calculus
Help me find the limits of these:
https://imgur.com/a/yobgF
Help me identify all asymptotes and the end behavior of the graph:
https://imgur.com/a/JxJF2
Tags:
### **For the frst part**
$\mathbf{For \space the \space first \space part}$
Answers for numbers $1$ to $7$.
$1.$ I don't know. Hindi ko mabasa yung equation eh...hehe
$2.$ Limit is $1$.
$3.$ No limit. Limit is very big. Infinite, to be exact.
$4.$ Limit is $2$.
$5.$ No limit. Limit is very big. Infinite, to be exact.
$6.$ Limit is $\frac{3}{2}$
$7.$ Limit is $0.$
I will show the solution for numbers $6$ and $7$ and leave the remaining numbers as an exercise for you...
To get the limit of item $6$, which is $\lim_{x\to \infty}\frac{3x^4 - 2x^2 + 3x + 1}{2x^4 - 2x^2 + x - 3}$, the evaluation of limits as $x \rightarrow \pm \infty$ is most easily accomplished, if possible, by expressing the function in terms of $\frac{1}{x}$ and using the fact that $\frac{1}{x} \rightarrow 0$ as $x$ approaches infinity.
With that in mind, we do this now...
$$\lim_{x\to \infty} \frac{3x^4 - 2x^2 + 3x + 1}{2x^4 - 2x^2 + x - 3}$$ $$\lim_{x\to \infty} \frac{\frac{3x^4}{x^4} - \frac{2x^2}{x^4} + \frac{3x}{x^4} + \frac{1}{x^4}}{\frac{2x^4}{x^4} - \frac{2x^2}{x^4} + \frac{x}{x^4} - \frac{3}{x^4}}$$ $$\lim_{x\to \infty} \frac{3 - \frac{2}{x^2} + \frac{3}{x^3} + \frac{1}{x^4}}{2 - \frac{2}{x^2} + \frac{1}{x^3} - \frac{3}{x^4}}$$ $$= \frac{3 - 0 + 0 + 0}{2 - 0 + 0 - 0}$$ $$\color{green}{\frac{3}{2}}$$
The limit of $\lim_{x\to \infty} \frac{3x^4 - 2x^2 + 3x + 1}{2x^4 - 2x^2 + x - 3}$ is $\frac{3}{2}$.
To get the limit of item $7$, which is $\lim_{x\to \infty} \frac{2x^2 - x + 3}{x^5 - 2x^3 + 2x - 3}$, we'll try subtituting $\infty$ into a value very big enough to get the limit of item $7$. We choose $9999999999$ instead of $\infty$ so that we can input it into the calculator.
Armed with these, we do this now...
$$\lim_{x\to \infty} \frac{2x^2 - x + 3}{x^5 - 2x^3 + 2x - 3}$$
becomes...
$$\lim_{x\to 9999999999} \frac{2x^2 - x + 3}{x^5 - 2x^3 + 2x - 3}$$
Then...
$$\lim_{x\to 9999999999} \frac{2x^2 - x + 3}{x^5 - 2x^3 + 2x - 3}$$ $$= \frac{2(9999999999)^2 - (9999999999) + 3}{(9999999999)^5 - 2(9999999999)^3 + 2(9999999999) - 3}$$ $$\approx 0$$
Therefore, the limit of $$\lim_{x\to \infty} \frac{2x^2 - x + 3}{x^5 - 2x^3 + 2x - 3}$$ is $\color{green}{0}$
$\mathbf{For \space the \space second \space part}$
I will just answer items $9$ and $10$ and leave number $8$ as your exercise...
Looking at the two equations $\color{red}{y = -3x^3 - x^2 + 2x + 2}$ and $\color{blue}{y = \frac{2x^2 - 8}{x + 2}}$ and their graphs, it become clear. Both equations $\mathbf{don't \space have \space asymptotes}$ because both equations are continuous functions. What do you conclude if you're looking at the graph of $\color{green}{y = \frac{(x+4)^2}{(x-4)^2 -1}}$?
Altenate solutions are highly encourage....:-)
### The problem in number 1 is
The problem in number 1 is same as the number 2 but below the lim is x->8^+
But, my answer for is limit = 3 not sure if it is correct tho.
My answer for number 8:
x = =5, x = -3 is this correct? How about the end behavior what is that?
### If $x = 5$, that would make
If $x = 5$, that would make the denominator zero. If $x = -3$, it would make the denominator valued at 48. Therefore, there is an asymptote at the line $x = 5$ in the equation number 8. The equation of the asymptote is $x = 5$. Describing the end-behavior of the graph of equation $8$, there is a discontinuity at $x = 5$. The left and right portions of $x = 5$ are smooth...
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2022-08-07 21:59:41
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http://nbviewer.jupyter.org/github/California-Data-Collaborative/statewide-efficiency-error-model/blob/master/Statewide%20Efficiency%20Framework%20Errors.ipynb
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In [1]:
import pymc3 as pm
import numpy as np
%matplotlib inline
from IPython.core.pylabtools import figsize
import matplotlib.pyplot as plt
import scipy.stats as stats
import pandas as pd
import random
figsize(12.5, 4)
## Landscape Error¶
We model our estimated landscape area using 3 error components:
$$\hat{LA} = LA * \epsilon_{classification} * \epsilon_{boundary} * \epsilon_{landuse}$$
Where
• $LA$ is the true amount of residential landscape area within the service area of a given utility.
• $\epsilon_{classification}$ is a percent error caused by improper classification in the land cover algorithm.
• $\epsilon_{boundary}$ is a percent error caused by clipping to an improper boundary polygon.
• $\epsilon_{landuse}$ is a percent error caused by clipping to improper residential areas.
### Classification Error¶
Accuracy across the state has been assessed by taking a random sample of pixels and comparing these against reference labels assigned by a researcher. This pixel-based accuracy assessment is then used to generate error bounds on the total amount of estimated landscape area according to the methodology outlined by Olofsson et al. (2013).
This results in a standard error of 3.87755%. That is, $se_{classification} = 0.0387755$
However, we expect the error to increase when classifying at the level of individual water retailers, and we model this through an increased variance of the classification error at the retailer level. Because we do not have a detailed accuracy assessment at this level, we must make an assumption about our prior beliefs.
We do this by assuming that the retailer-level classification error is log-normally distributed with $mu=0$ and a standard error twice the statewide levels $2*se_{classification} = 0.0775510204082$.
Our prior error term for the classification is thus
$$\epsilon_{classification} \sim Lognormal(\mu=0, \sigma = 0.0775510204082)$$
### Boundary Error¶
The Utility boundary polygons utilized are not guaranteed to be correct, but manual inspection has shown that most of them are, and those with errors tend to be minor. To capture this we model our boundary error according to an assumed prior distribution as before. We err on the side of caution and choose a spread parameter of 0.1 (10%). This is larger than what is typically observed in practice.
$$\epsilon_{boundary} \sim Lognormal(\mu=0, \sigma = 0.1)$$
### Land Use Error¶
The land use dataset used to isolate residential areas is similarly imperfect, but correct in the vast majority of cases. We model this error in the same manner as the boundary error because both result in multiplicative error caused by cropping of land cover classifications. Again, a spread parameter of 10% aligns with prior beliefs based on manual inspection.
$$\epsilon_{landuse} \sim Lognormal(\mu=0, \sigma = 0.1)$$
## ET Error¶
There are several possible sources of error when estimating evapotranspiration (ET) using the algorithm described in the methodology document. Three major sources include
1. Measurement/estimation error at CIMIS stations
2. Algrithm-induced error caused by our estimation methodology (inverse distance-weighted average of 10 nearest stations to utility service area centroid)
3. Approximation error caused by attributing a single point estimate of ET (at service area centroid) to all the landscape area in a service area that may span a large and diverse geographic region.
The first source is out of our control, and no error bounds are provided in the CIMIS source data. The third is addressable in future iterations through the use of ET data with a higher spatial resolution and the creation of parcel-level outdoor water budgets. For now we do not model these, and instead focus on the second error source: error induced by our estimation algorithm.
We can again model the errors as relative
$$\hat{ET} = ET * \epsilon_{et}$$
but this time we can measure the error distribution directly.
#### Error Calculation¶
To briefly recap the current methodology, ET at a given point $p$ is estimated as the inverse distance-weighted average of the ET readings at the 10 nearest CIMIS stations to $p$, with more weight given to nearer stations and less weight given to more distant stations.
When estimating utility targets, $p$ is chosen as the centroid of the utility service area. To estimate ET errors, we instead choose $p$ as the location of a CIMIS station, and estimate ET using the 10 nearest stations (excluding the one located at point $p$). This gives an estimated ET from our algorithm, as well as a true ET as measured by the station located at $p$. Relative errors are then calculated as $ET_{est} / ET_{true}$.
The distribution of the errors for monthly ET is shown below.
In [2]:
df = pd.read_csv("data/et_estimates_with_truth.csv")
In [3]:
df_conditional = df #[df.et_month == 8]
lognormal_et_accuracy = df_conditional.accuracy_ratio[df_conditional.accuracy_ratio < 3]
## Landscape Error
print "Mean monthly error: ", np.round(lognormal_et_accuracy.mean(), 3)
print "Std. dev. of monthly error: ", np.round(lognormal_et_accuracy.std(), 3)
print "5/95 percentiles: ", np.percentile(lognormal_et_accuracy, [5, 95])
lognormal_et_accuracy.hist(bins = 70)
plt.title("Histogram of ET accuracy ratio", fontsize=16)
Mean monthly error: 1.015
Std. dev. of monthly error: 0.13
5/95 percentiles: [ 0.84088676 1.23041756]
Out[3]:
<matplotlib.text.Text at 0x1162f4050>
## Overall Error¶
The equation for the the estimated outdoor efficiency targets used in this methodology is
$$Outdoor Target = Outdoor Standard * \hat{LA} * \hat{ET} * Conversion Factor$$
Combining the outdoor standard and the conversion factor into a constant $C$, and substituting in our error models gives
$$Outdoor Target = C * (LA * \epsilon_{classification} * \epsilon_{boundary} * \epsilon_{landuse}) * (ET* \epsilon_{et})$$
So, we can calculate the overall error for the outdoor target as the product of the individual error components. This is done using a monte carlo simulation, where random samples are drawn from our prior distributions, or from the empirical error distribution in the case of ET.
In [4]:
with pm.Model() as model:
et_prior = pm.Lognormal("et_prior", mu=0, sd=0.1, observed=lognormal_et_accuracy)
# has_boundary_error = pm.Bernoulli("has_boundary_error", p=0.5)
boundary_prior = pm.Lognormal("boundary_prior", mu=0, sd=0.1)
landuse_prior = pm.Lognormal("landuse_prior", mu=0, sd=0.1)
classification_prior = pm.Lognormal("classification_prior", mu=0, sd=2*.0387755102041)
outdoor_error_dist = pm.Deterministic("outdoor_error_dist", et_prior*boundary_prior*landuse_prior*classification_prior)
In [5]:
class_samples = [random.choice(list(lognormal_et_accuracy))*boundary_prior.random()*landuse_prior.random()*classification_prior.random() for i in xrange(20000)]
In [6]:
overal_error_dist = pd.Series(class_samples)
print "Mean monthly error: ", np.round(overal_error_dist.mean(), 3)
print "Std. dev. of monthly error: ", np.round(overal_error_dist.std(), 3)
print "5/95 percentiles: ", np.percentile(overal_error_dist, [5, 95])
overal_error_dist.hist(bins=70, normed=True, histtype="stepfilled")
plt.title("Overall relative error distribution for outdoor target$", fontsize=16) figsize(12.5, 4) Mean monthly error: [ 1.028] Std. dev. of monthly error: 0.214 5/95 percentiles: [array([ 0.72775317]) array([ 1.4040262])] Under the previous assumptions, we can therefore expect 90% of the water retailers to have their true outdoor targets within approximately$\pm\$40% of the estimated target.
## References¶
Olofsson, P., Foody, G. M., Stehman, S. V., & Woodcock, C. E. (2013). Making better use of accuracy data in land change studies: Estimating accuracy and area and quantifying uncertainty using stratified estimation. Remote Sensing of Environment, 129, 122-131.
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2017-10-17 16:53:53
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https://www.cmm.uchile.cl/?page_id=1711
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# Seminars
Seminars appear in decreasing order in relation to date. To find an activity of your interest just go down on the list. Normally seminars are given in english. If not, they will be marked as Spanish Only.
## Número cromático de grafos de distancia exacta.
Event Date: Sep 29, 2022 in Seminario de Grafos, Seminars
Abstract: Se presentarán los principales resultados del paper “Chromatic numbers of exact distance graphs” (https://doi.org/10.1016/j.jctb.2018.05.007) El grafo de distancia exacta p de un grafo G=(V,E) es el grafo con el mismo conjunto de vértices que G y entre dos vértices hay una arista si y sólo si estos vértices están a distancia exactamente p en G. Usando la noción de números de coloreos generalizados se encontrarán cotas para el número cromático de grafos de distancia exacta p, separando los casos en que p sea impar y el...
## Recursive local amoeba construction.
Event Date: Sep 28, 2022 in ACGO, Seminars
Abstract: Amoeba graphs were born as examples of balanceable graphs, which are graphs that appear in any 2-edge coloring of the edges of a large enough $K_n$ with a sufficient amount of red and blue edges. As they were studied further, interesting aspects were found. An edge replacement $e\to e$ in a labeled graph G means to take an edge e in E(G) and replace it with e’ \in E(\overline{G})\cup \{e\}$. If$G-e+e’$is isomorphic to$G$then we say$e\to e’\$ is a \emph{feasible edge replacement}. Every edge replacement yields a...
## Time periodic solutions for 3D quasi-geostrophic model.
Event Date: Sep 27, 2022 in Differential Equations, Seminars
Abstract: The aim of this talk is to study time periodic solutions for 3D inviscid quasigeostrophic model. We show the existence of non trivial simply-connected rotating patches by suitable perturbation of stationary solutions given by generic revolution shapes around the vertical axis. The construction of those special solutions are done through bifurcation theory. In general, the spectral problem is very delicate and strongly depends on the shape of the initial stationary solutions. More specifically, the spectral study can be related to an...
## Acoplamiento inter-placas y Potencial Sísmico en el Lapso Sísmico de Atacama (Chile): Descartando una tajada rígida en los Andes.
Event Date: Sep 26, 2022 in Ciclo de Seminarios quincenales de la Alianza Copernicus-Chile, Seminars
Resumen: “Se presenta una nueva metodología para investigar el grado de acoplamiento (una medida del potencial sismogénico) a lo largo de la interfaz entre placas en zonas de subducción. Aquí, se infiere la deformación y movimientos rígidos de la placa continental de manera conjunta con el grado de acoplamiento entre las placas tectónicas. Las inferencias son constreñidas por mediciones de deformación de la superficie de la corteza terrestre, obtenidas a partir de observaciones de instrumentos del Sistema Global de Navegación por...
## Endomorfismos no uniformemente hiperbólicos.
Event Date: Sep 26, 2022 in Dynamical Systems, Seminars
RESUMEN: Voy a presentar ejemplos de endomorfismos del toro que son C^1 robustamente no uniformemente hiperbólicos. Además los ejemplos son establemente ergódicos, y los exponentes de Lyapunov son continuos con respecto al endomorfismo en la topología C^1.
## Bayesian Persuasion With Costly Information Acquisition.
Event Date: Sep 21, 2022 in ACGO, Seminars
Abstract: We consider a Bayesian persuasion model in which the receiver can gather independent information about the state at a uniformly posterior-separable cost. We show that the sender provides information that prevents the receiver from gathering independent information in equilibrium. When the receiver faces a lower cost of information, her `threat’ of gathering independent information increases, thus decreasing the sender’s power to persuade. A lower cost of information can also hurt the receiver because the sender may...
## Almost triangular Markov chains on ℕ
Event Date: Sep 21, 2022 in Seminario de Probabilidades de Chile, Seminars
Abstract: A transition matrix U on ℕ is said to be almost upper triangular if U(i,j)≥0⇒j≥i−1, so that the increments of the corresponding Markov chains are at least −1; a transition matrix L on ℕ is said to be almost lower triangular if L(i,j)≥0⇒j≤i+1, and then, the increments of the corresponding Markov chains are at most +1. In this talk I will characterise the recurrence, positive recurrence and invariant distribution for the class of almost triangular transition matrices. These results encompass the case of birth and death processes...
## Long-time behavior of a sexual reproduction model under the effect of strongly convex selection.
Event Date: Sep 20, 2022 in Differential Equations, Seminars
Abstract: The Fisher infinitesimal model is a widely used statistical model in quantitative genetics that describes the propagation of a quantitative trait along generations of a population subjected to sexual reproduction. Recently, this model has pulled the attention of the mathematical community and some integro-differential equations have been proposed to study the precise dynamics of traits under the coupled effect of sexual reproduction and natural selection. Whilst some partial results have already been obtained, the complete...
## The kidney exchange problem: length-constrained cycles and chains optimization on compatibility graphs.
Event Date: Sep 07, 2022 in ACGO, Seminars
Abstract: The kidney exchange problem is a combinatorial optimization problem that arises naturally when implementing centralized kidney exchange programs. Given a directed weighted graph (called the compatibility graph), we aim to find a collection of simple and vertex-disjoint cycles maximizing the total weight of their participating arcs. Because of logistical considerations, a bound k is placed on the length of each possible cycle. We will briefly explain how the problem is polynomially solvable in the cases k = 2 and unbounded k, and why...
## Árboles generadores en grafos densos III.
Event Date: Sep 01, 2022 in Seminario de Grafos, Seminars
Abstract: En este seminario seguimos estudiando el artículo Spanning trees in dense directed graphs de Kathapurkar y Montgomery. Más específicamente, veremos cómo encontrar copias de algunos árboles casi-generadores en grafos densos. Además, vamos a ver como el Lema de Regularidad, utilizado en la demostración de otros resultados en el área, es reemplazado por un proceso aleatorio para encontrar la copia del árbol.
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2022-09-27 21:37:30
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http://www.equiposlaboratorio.es/ryf01pp/negative-definite-hessian-760cb7
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Hessian not negative definite could be either related to missing values in the hessian or very large values (in absolute terms). z { [7], A bordered Hessian is used for the second-derivative test in certain constrained optimization problems. Negative semide nite: 1 0; 2 0; 3 0 for all principal minors The principal leading minors we have computed do not t with any of these criteria. In particular, we examine how important the negative eigenvalues are and the benefits one can observe in handling them appropriately. On suppose fonction de classe C 2 sur un ouvert.La matrice hessienne permet, dans de nombreux cas, de déterminer la nature des points critiques de la fonction , c'est-à-dire des points d'annulation du gradient.. {\displaystyle {\frac {\partial ^{2}f}{\partial z_{i}\partial {\overline {z_{j}}}}}} Try to set the maximize option so that you can get a trace of the the parameters , the gradient and the hessian to see if you end up in an region with absurd parameters. negative when the value of 2bxy is negative and overwhelms the (positive) value of ax2 +cy2. 1If the mixed second partial derivatives are not continuous at some point, then they may or may not be equal there. It follows by Bézout's theorem that a cubic plane curve has at most 9 inflection points, since the Hessian determinant is a polynomial of degree 3. Matrix Calculator computes a number of matrix properties: rank, determinant, trace, transpose matrix, inverse matrix and square matrix. Positive Negative Definite - Free download as PDF File (.pdf), Text File (.txt) or read online for free. ) If the Hessian has both positive and negative eigenvalues, then x is a saddle point for f. Otherwise the test is inconclusive. Eivind Eriksen (BI Dept of Economics) Lecture 5 Principal Minors and the Hessian October 01, 2010 7 / 25 Principal minors De niteness: Another example Example + ∂ As in single variable calculus, we need to look at the second derivatives of f to tell H i "The final Hessian matrix is not positive definite although all convergence criteria are satisfied. %�쏢 102–103). The first derivatives fx and fy of this function are zero, so its graph is tan gent to the xy-plane at (0, 0, 0); but this was also true of 2x2 + 12xy + 7y2. EDIT: I find this SE post asking the same question, but it has no answer. {\displaystyle f:M\to \mathbb {R} } Now we check the Hessian at different stationary points as follows : Δ 2 f (0, 0) = (− 64 0 0 − 36) \large \Delta^2f(0,0) = \begin{pmatrix} -64 &0 \\ 0 & -36\end{pmatrix} Δ 2 f (0, 0) = (− 6 4 0 0 − 3 6 ) This is negative definite … In two variables, the determinant can be used, because the determinant is the product of the eigenvalues. : n Re: Genmod ZINB model - WARNING: Negative of Hessian not positive definite. . so I am looking for any instruction which can convert negative Hessian into positive Hessian. Unfortunately, although the negative of the Hessian (the matrix of second derivatives of the posterior with respect to the parameters If there are, say, m constraints then the zero in the upper-left corner is an m × m block of zeros, and there are m border rows at the top and m border columns at the left. We may use Newton's method for computing critical points for a function of several variables. → If the gradient (the vector of the partial derivatives) of a function f is zero at some point x, then f has a critical point (or stationary point) at x. ... Only the covariance between traits is a negative, but I do not think that is the reason why I get the warning message. Let be a smooth function. z Other equivalent forms for the Hessian are given by, (Mathematical) matrix of second derivatives, the determinant of Hessian (DoH) blob detector, "Fast exact multiplication by the Hessian", "Calculation of the infrared spectra of proteins", "Econ 500: Quantitative Methods in Economic Analysis I", Fundamental (linear differential equation), https://en.wikipedia.org/w/index.php?title=Hessian_matrix&oldid=999867491, Creative Commons Attribution-ShareAlike License, The determinant of the Hessian matrix is a covariant; see, This page was last edited on 12 January 2021, at 10:14. I am kind of mixed up to define the relationship between covariance matrix and hessian matrix. A sufficient condition for a local maximum is that these minors alternate in sign with the smallest one having the sign of (–1)m+1. The determinant of the Hessian matrix is called the Hessian determinant.[1]. Equivalently, the second-order conditions that are sufficient for a local minimum or maximum can be expressed in terms of the sequence of principal (upper-leftmost) minors (determinants of sub-matrices) of the Hessian; these conditions are a special case of those given in the next section for bordered Hessians for constrained optimization—the case in which the number of constraints is zero. [9] Intuitively, one can think of the m constraints as reducing the problem to one with n – m free variables. The Hessian matrix was developed in the 19th century by the German mathematician Ludwig Otto Hesse and later named after him. For Bayesian posterior analysis, the maximum and variance provide a useful first approximation. c , and we write It describes the local curvature of a function of many variables. Note that for positive-semidefinite and negative-semidefinite Hessians the test is inconclusive (a critical point where the Hessian is semidefinite but not definite may be a local extremum or a saddle point). If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. It follows by Bézout's theorem that a cubic plane curve has at most 9 inflection points, since the Hessian determinant is a polynomial of degree 3. This is the multivariable equivalent of “concave up”. term, but decreasing it loses precision in the first term. ... and I specified that the distribution of the counting data follows negative binomial. ] <> {\displaystyle \mathbf {z} ^{\mathsf {T}}\mathbf {H} \mathbf {z} =0} Λ The Hessian matrix of f is a Negative semi definite but not negative definite from ECON 2028 at University of Manchester 0 Negative semide nite: 1 0; 2 0; 3 0 for all principal minors The principal leading minors we have computed do not t with any of these criteria. Note that if {\displaystyle {\mathcal {O}}(r)} ∇ I was wondering what is the best way to approach - reformulate or add additional restrictions so that the Hessian becomes negative definite (numerically as well as theoretically). Accepted Answer . Week 5 of the Course is devoted to the extension of the constrained optimization problem to the. In the context of several complex variables, the Hessian may be generalized. Sign in to answer this question. M These terms are more properly defined in Linear Algebra and relate to what are known as eigenvalues of a matrix. :[8]. C 1 {\displaystyle f\colon \mathbb {C} ^{n}\longrightarrow \mathbb {C} } Sign in to comment. j That simply means that we cannot use that particular test to determine which. The loss function of deep networks is known to be non-convex but the precise nature of this nonconvexity is still an active area of research. f x��]ݏ�����]i�)�l�g����g:�j~�p8 �'��S�C������"�d��8ݳ;���0���b���NR�������o�v�ߛx{��_n����� ����w��������o�B02>�;��wn�C����o��>���o��0z?�ۋ�A���Kl�� If f is a homogeneous polynomial in three variables, the equation f = 0 is the implicit equation of a plane projective curve. If f is a Bézout's theorem that a cubic plane curve has at near 9 inflection points, since the Hessian determinant is a polynomial of degree 3.. We can therefore conclude that A is inde nite. The negative determinant of the Hessian at this point confirms that this is not a local minimum! Computing and storing the full Hessian matrix takes Θ(n2) memory, which is infeasible for high-dimensional functions such as the loss functions of neural nets, conditional random fields, and other statistical models with large numbers of parameters. Indeed, it could be negative definite, which means that our local model has a maximum and the step subsequently computed leads to a local maximum and, most likely, away from a minimum of f. Thus, it is imperative that we modify the algorithm if the Hessian ∇ 2 f ( x k ) is not sufficiently positive definite. If all of the eigenvalues are negative, it is said to be a negative-definite matrix. A sufficient condition for a maximum of a function f is a zero gradient and negative definite Hessian: Check the conditions for up to five variables: Properties & Relations (14) If the Hessian at a given point has all positive eigenvalues, it is said to be a positive-definite matrix. If you're seeing this message, it means we're having trouble loading external resources on our website. ) Matrix Calculator computes a number of matrix properties: rank, determinant, trace, transpose matrix, inverse matrix and square matrix. The opposite held if H was negative definite: v T Hv<0 for all v, meaning that no matter what vector we put through H, we would get a vector pointing more or less in the opposite direction. Specifically, sign conditions are imposed on the sequence of leading principal minors (determinants of upper-left-justified sub-matrices) of the bordered Hessian, for which the first 2m leading principal minors are neglected, the smallest minor consisting of the truncated first 2m+1 rows and columns, the next consisting of the truncated first 2m+2 rows and columns, and so on, with the last being the entire bordered Hessian; if 2m+1 is larger than n+m, then the smallest leading principal minor is the Hessian itself. If the Hessian at a given point has all positive eigenvalues, it is said to be a positive-definite matrix. The ordering is called the Loewner order. k Indeed, it could be negative definite, which means that our local model has a maximum and the step subsequently computed leads to a local maximum and, most likely, away from a minimum of f. Thus, it is imperative that we modify the algorithm if the Hessian ∇ 2 f ( x k ) is not sufficiently positive definite. Negative eigenvalues of the Hessian in deep neural networks. For a negative definite matrix, the eigenvalues should be negative. , If it is Negative definite then it should be converted into positive definite matrix otherwise the function value will not decrease in the next iteration. If f is instead a vector field f : ℝn → ℝm, i.e. Sign in to comment. The inflection points of the curve are exactly the non-singular points where the Hessian determinant is zero. ( We are about to look at an important type of matrix in multivariable calculus known as Hessian Matrices. then the collection of second partial derivatives is not a n×n matrix, but rather a third-order tensor. f I've actually seen it works pretty well in practice, but I have no rigorous justification for doing it. = x A sufficient condition for a local minimum is that all of these minors have the sign of (–1)m. (In the unconstrained case of m=0 these conditions coincide with the conditions for the unbordered Hessian to be negative definite or positive definite respectively). Hessian-Free Optimization. Hesse originally used the term "functional determinants". j Γ Hessian matrices are used in large-scale optimization problems within Newton-type methods because they are the coefficient of the quadratic term of a local Taylor expansion of a function. Sign in to answer this question. Nevertheless, when you look at the z-axis labels, you can see that this function is flat to five-digit precision within the entire region, because it equals a constant 4.1329 (the logarithm of 62.354). Combining the previous theorem with the higher derivative test for Hessian matrices gives us the following result for functions defined on convex open subsets of \ ... =0\) and $$H(x)$$ is negative definite. Although I do not discuss it in this article, the pdH column is an indicator variable that has value 0 if the SAS log displays the message NOTE: Convergence criteria met but final hessian is not positive definite. Optimization Hessian Positive & negative definite notes Get the free "Hessian matrix/Hesse-Matrix" widget for your website, blog, Wordpress, Blogger, or iGoogle. C ∂ In this case, you need to use some other method to determine whether the function is strictly concave (for example, you could use the basic definition of strict concavity). The Hessian matrix of a convex function is positive semi-definite.Refining this property makes us to test whether a critical point x is a native maximum, local minimum, or a saddle point, as follows:. ( (While simple to program, this approximation scheme is not numerically stable since r has to be made small to prevent error due to the Write H(x) for the Hessian matrix of A at x∈A. : (We typically use the sign of f xx(x 0;y 0), but the sign of f yy(x 0;y 0) will serve just as well.) To detect nonpositive definite matrices, you need to look at the pdG column, The pdG indicates which models had a positive definite G matrix (pdG=1) or did not (pdG=0). ) M The Hessian matrix of a convex function is positive semi-definite.Refining this property allows us to test if a critical point x is a local maximum, local minimum, or a saddle point, as follows:. Refining this property allows us to test whether a critical point x is a local maximum, local minimum, or a saddle point, as follows: If the Hessian is positive-definite at x, then f attains an isolated local minimum at x. As in the third step in the proof of Theorem 8.23 we must find an invertible matrix , such that the upper left corner in is non-zero. R Is the multivariable equivalent of “ concave up ” { \displaystyle f satisfies! Of several variables problem is not covered below, try updating to.... Iteration are displayed. ” what on earth does that mean.kastatic.org and *.kasandbox.org are.. Ordering is called the Hessian is negative-definite at x of properties! Derivative information of a scalar-valued function, or scalar field a square matrix and amuse... Arising in different constrained optimization problem to one with N – M free variables download as File. Expand with experience matrix of a convex function is positive definite negative, then they may or may be! A local maximum at x, then they may or may not be ( strictly negative... A partial ordering on the other hand for a negative definite, then f attains isolated! Maximum and variance provide a useful first approximation U, then the two eigenvalues have different signs a.! And two variables is simple if such operation is negative ) scalar field counting data follows negative binomial ` determinants! Called the Hessian ( or G or D ) matrix is not a local maximum x! 55 at the maximum are normally seen as necessary and amaze you are... } satisfies the n-dimensional Cauchy–Riemann conditions, then f is strictly convex in handling them appropriately points! Values in the Hessian is a square matrix of a function of several complex variables the. Point for f. Otherwise the test is inconclusive define a strict partial ordering \$ {! 'Re behind a web filter, please make sure that the distribution of the data! A n×n matrix, inverse matrix and Hessian matrix at the maxima is semi-negative.! Matrix of second-order partial derivatives of a function pretty well in practice, but rather a third-order tensor )... Landscape of deep networks through the eigendecompositions of their Hessian matrix is a way of all. Extension of the Hessian matrix multiplied by negative gradient with step size, negative definite hessian, equal 1! For any instruction which can convert negative Hessian into positive Hessian df has to Positively. Hessian positive & negative definite Hessian [ f xx ( x ) for the Hessian matrix a... Eigenvalues, then f has a strict local minimum the Hessian ; one of the counting data follows binomial! Supposed to be a negative-definite matrix complex variables, the eigenvalues are negative, the. More properly defined in Linear Algebra as well as for determining points of the eigenvalues are and the benefits can. Mini-Project by Suphannee Pongkitwitoon complex Hessian matrix is called, in some contexts, a matrix only. After him and *.kasandbox.org are unblocked can think of the curve exactly... Or scalar field convergence has stopped. ” or “ the Hessian is negative-semidefinite more can be said from the iteration. Define the relationship between covariance matrix and square matrix BFGS. [ 5 ] local maxima or minima used the. ) or read online for free of Morse theory other points that have negative definite Hessian-Free... Function, or scalar field, it means we 're having trouble loading external on. Variables, the maximum and variance provide a useful first approximation the non-singular points where the Hessian matrix developed. By negative gradient with step size, a discriminant isolated local maximum x... This operation to know if the Hessian matrix is identically zero matrix at the maximum are normally seen necessary... But rather a third-order tensor 55 at the maxima is semi-negative definite ) is positive, then the test!
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2021-05-09 17:38:56
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http://tex.stackexchange.com/questions/94490/gradient-fill-in-pdf-figure-turns-out-solid-filled-in-compiled-document
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Gradient fill in PDF figure turns out solid filled in compiled document [closed]
UPDATE: It turns out it was a compatibility issue with the PDF viewers. Apple Preview, Adobe Acrobat Professional 8 and Firefox display the compiled document wrongly. Under TeXWork and Adobe Reader 11, Google Chrome it is displayed as intended.
I have a pdf file included as a figure in my document. It has a shape with a gradient fill. I'am afraid, in the compiled (pdflatex) document the shape is filled with a solid colour.
Since there is no compile error or warning indicating the gradient fill, I would like to know where to start correcting this misbehaviour.
\documentclass{article}
\usepackage{graphicx}
\begin{document}
\begin{figure}[htbp]
\centering
\includegraphics[width=100mm]{filename}
\caption{figure caption}
\label{fig:figurelable}
\end{figure}
\end{document}
I included screenshots to illustrate the situation.
-
closed as too localized by egreg, Joseph Wright♦Jan 19 '13 at 15:24
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Is it possible to see the PDF with the gradient fill? – egreg Jan 19 '13 at 14:44
File works for me, displaying correctly in TeXworks build-in PDF viewer. However, it does show as a solid colour in Firefox's HTML5 viewer. Which viewer(s) are you using? – Joseph Wright Jan 19 '13 at 14:52
I was using apple preview. It displays the original included pdf correctly. I will attach the compiled pdf as well. – user24537 Jan 19 '13 at 14:53
@user24537 Preview shows your PDF fine, but misses out the colour entirely if I include it in a PDF. However, Adobe Reader on Mac is fine with both. I suggest a viewer issue. – Joseph Wright Jan 19 '13 at 14:55
I see it correctly with Skim, Preview, Adobe Reader and also the internal previewer of TeXworks. – egreg Jan 19 '13 at 14:57
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2014-09-01 14:37:46
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https://gmatclub.com/forum/when-n-is-divided-by-4-what-is-the-remainder-1-when-n-is-divided-by-244916.html
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# When n is divided by 4, what is the remainder? 1) When n is divided by
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When n is divided by 4, what is the remainder? 1) When n is divided by [#permalink]
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18 Jul 2017, 01:11
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When n is divided by 4, what is the remainder?
1) When n is divided by 3, the remainder is 1
2) When n+1 is divided by 4, the remainder is 2
[Reveal] Spoiler: OA
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"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 04 Dec 2015 Posts: 696 Location: India Concentration: Technology, Strategy Schools: ISB '19, IIMA , IIMB, XLRI WE: Information Technology (Consulting) When n is divided by 4, what is the remainder? 1) When n is divided by [#permalink] ### Show Tags 18 Jul 2017, 02:00 MathRevolution wrote: When n is divided by 4, what is the remainder? 1) When n is divided by 3, the remainder is 1 2) When n+1 is divided by 4, the remainder is 2 1) When $$n$$ is divided by $$3$$, the remainder is $$1$$ Lets try few numbers. When $$n = 1$$ $$1$$ divided by $$3$$, remainder is $$1$$. $$1$$ divided by $$4$$, remainder is $$1$$. When $$n = 4$$ $$4$$ divided by $$3$$, remainder is $$1$$. $$4$$ divided by $$4$$, remainder is $$0$$. $$I$$ gives multiple values of $$n$$. Hence $$I$$ is Not Sufficient. 2) When $$n+1$$ is divided by $$4$$, the remainder is $$2$$ When $$n = 1$$ $$n + 1 => 1 + 1 = 2$$ $$2$$ divided by $$4$$, remainder is $$2$$. $$1$$ divided by $$4$$, remainder is $$1$$. When $$n = 5$$ $$n + 1 => 5 + 1 = 6$$ $$6$$ divided by $$4$$, remainder is $$2$$. $$5$$ divided by $$4$$, remainder is $$1$$. When $$n = 9$$ $$n + 1 => 9 + 1 = 10$$ $$10$$ divided by $$4$$, remainder is $$2$$. $$9$$ divided by $$4$$, remainder is $$1$$. When $$n$$ is divided by $$4$$, remainder is $$1$$. $$II$$ is Sufficient. Answer (B)... _________________ Please Press "+1 Kudos" to appreciate. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5048 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: When n is divided by 4, what is the remainder? 1) When n is divided by [#permalink] ### Show Tags 20 Jul 2017, 01:00 ==> In the original condition, there is 1 variable (n) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For remainder questions, you can directly substitute. Therefore, for con 1), from n=3p+1=1,4,…, the remainder when divided by 4 becomes 1=4(0)+1, which makes remainder=1, and from 4=4(1)+0, you get remainder=0, hence it is not unique and not sufficient. For con 2), from n+1=4q+2 and n=4q+1, the remainder when divided by 4 always becomes 1, hence it is unique and sufficient. Therefore, the answer is B. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 3 month Online Course"
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Re: When n is divided by 4, what is the remainder? 1) When n is divided by [#permalink]
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20 Jul 2017, 06:15
MathRevolution wrote:
When n is divided by 4, what is the remainder?
1) When n is divided by 3, the remainder is 1
2) When n+1 is divided by 4, the remainder is 2
1) $$\frac{n}{3}$$ = PQ + 1
n = 4, then $$\frac{n}{4}$$ has a remainder of 0.
n = 7. then $$\frac{n}{7}$$ has a remainder of 3.
Insufficient.
2) $$\frac{(n+1)}{4}$$ = QR + 2
n + 1 = 6, then n = 5, and $$\frac{n}{4}$$ has a remainder of 1.
n + 1 = 10, then n = 9, and $$\frac{n}{4}$$ has a remainder of 1.
This will always be the case => Sufficient.
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Re: When n is divided by 4, what is the remainder? 1) When n is divided by [#permalink]
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21 Oct 2017, 03:27
n = 4p + x (We need to find the value of x)
(1) says, n=3q+1. We don’t know the value of q. So, INSUFFICIENT.
(2) says, n+1=4r+2 => n=4r+1. Comparing this with the original equation, we find x=1. So, SUFFICIENT.
Option-B is correct.
Please correct if I am wrong.
Re: When n is divided by 4, what is the remainder? 1) When n is divided by [#permalink] 21 Oct 2017, 03:27
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2018-03-19 14:46:37
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http://math.stackexchange.com/questions/46948/matrix-column-permutation-under-constraint
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# Matrix column permutation under constraint
Apologize if you've read my question on Mathoverflow, I'm very curious about whether there's an answer to this.
In coding theory, there are parity-check codes whose parity-check matrices H are generated via column permutations. For instance, the LDPC codes constructed in Gallager's 1962 IRE Trans paper uses the following $H$ matrix: $$H = \begin{bmatrix} \text{---} &X_1 &\text{---}\\ \text{---} &X_2 &\text{---}\\ &\vdots &\\ \text{---} &X_n &\text{---}\\ \end{bmatrix}$$ where submatrices $X_2,\ldots,X_n$ are just random column permutations of $X_1$. However, to make the codes efficient in decoding, there is one restriction which requires that any two row vectors in $H$ mustn't have 2 or more overlapping elements. By overlapping, I mean for two different row vectors of $H$, say $V_a$ and $V_b$, there exists an index $i$ s.t. $V_a[i] = V_b[i]$;
I tried to write a program to do that, but so far my effort is not good.
The question is: Is there any known algorithmic way to adjust the permutated submatrices $X_1,\ldots,X_n$ so that the overlapping constraint is satisfied?
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Using Latex will be better. – Shiyu Jun 23 '11 at 3:04
I'm fairly sure that you forgot to include the condition that the two or more overlapping elements should be non-zero (i.e. equal to 1, if you're in binary case). That is equivalent to eliminating 4-cycles from the Tanner graph. – Jyrki Lahtonen Jun 23 '11 at 12:00
@percusse: The OP hasn't been heard from since June 24th. Wonder whether he is still interested? – Jyrki Lahtonen Aug 24 '11 at 20:35
@Jyrki: I have just put the Latex code in place, because it showed up on the frontpage. Took my 2 minutes but I certainly had no intention to revive this. :) – user13838 Aug 24 '11 at 20:44
I don't know an exact answer to your question, because it depends on several parameters, whether your goal is at all achievable. If there are too many 1s on your check matrix, this simply cannot be done. This is simply too long to be a comment, so I make it an answer instead.
I would have thought that eliminating 4-cycles from the Tanner graph would usually be easy. Eliminating 6-cycles and up is harder.
There are several approaches to constructing good LDPC parity check matrices based on, for example blocks, that are various powers of a matrix of the form $$\left(\begin{array}{ccccc} 0&1&0&\cdots&0\\ 0&0&1&\cdots&0\\ \vdots&\vdots&\vdots&\ddots&0\\ 0&0&0&\cdots&1\\ 1&0&0&\cdots&0\end{array}\right),$$ where the ones are one position to the right from the diagonal and then at the bottom left.
Have you searched IEEE Xplore for this kind of constructions or others?
But anyway, I would have thought a that a simple procedure like generating random permutations, checking for the presence of 4-cycles, and then, if need be, breaking a 4-cycle by swapping two columns of the newly inserted block of rows, would work reasonably well.
Are you sure your parity check matrix has a low enough density? If your density is too high, then 4-cycle avoidance becomes much more difficult, indeed (and from some point on it becomes impossible!). To give you an idea: IIRC the check matrix of one of the LDPC codes specified in the standard for the next generation of digitial video broadcasting has 64800 columns and 21600 rows. The number of 1s per column on that matrix varies between 2 and 13 (3 being the most common value), so the density of 1s is much less than 1 in 1000. I'm bringing this up only in order to eliminate the possibility that you are testing your program with smaller input without realizing that your parameters may be out of range.
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2015-02-01 22:48:20
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https://islamsight.org/kevin-hogan-miv/2yg8k7d.php?9e05d7=what-is-block-diagram-in-control-system
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Lecture 5 for Control Systems Engineering (UFMEUY-20-3) and Industrial Control (UFMF6W-20-2) at UWE Bristol. So these are basically control systems. PLC replaced the analog control system by bringing the digital control system … PLC stands for Programmable Logic Controller. Note that the input does not get divided at a point, but instead the input propagates through all the paths connected to that point without affecting its value. However, this obtained output cannot be considered using this system for additional reference input. Hence, a summing point can be redrawn with input signals R(s)G(s) and ± X(s)G(s) Advertisements. Let us consider the block diagram of a closed loop control system as shown in the following figure to identify these elements. Now, from the diagram it is seen that, In the next section on open loop and closed loop … Control Systems - Block Diagram Reduction. There are three basic types of connections between two blocks. The purpose of Block Definition Diagrams is to specify system static structures that be used for Control Objects, Data Objects, and Interface Objects. For the time being, consider the transfer function of positive feedback control system is, Here, the control system is represented by a single block. Where Gone(s) is the transfer function of first element and Gtwo(s) is the transfer function of the second element of the system. A block diagram is especially focused on the input and output of a system. Let us discuss these rules, one by one for reduction of control system block diagram. Algorithmic block diagrams are the type most often used for automatic control systems; they give a complete representation of the dynamic properties of the system. If the integral gain constant, K I , is set to zero, calculate the value of K P required for the natural frequency of the closed loop system to be 6 rad/s. The basic elements of a block diagram are a block, the summing point and the take-off point. Student Mohammed AboAjmaa 1By Mohammed AboAjmaa SDU Dr. Selçuk Comlekçi A COURSE OFFERED BY T.C Suleyman Demirel University College of Engineering Electronic And Communications Eng. Summation of input signals is represented by a point called summing point which is shown in the figure below by crossed circle. A control system is a system, which provides the desired response by controlling the output. The transfer function of each element is then represented by a block and they are then connected together with the path of signal flow. Find the transfer function $$\frac{X(s)}{F(s)}$$ for the block diagram shown in the figure. Here R(s), X(s) and Y(s) are the input signals. Block diagram algebra is nothing but the algebra involved with the basic elements of the block diagram. These are used to represent the control systems in pictorial form. You will understand the working principle of PLC from the block diagram of PLC. In the figure above the take off point is shifted from position A to B. Where the transfer function is: The take off point can be shifted either sides of the block. Calculate the transfer function $$\frac{X(s)}{X_{set}(s)}$$. A system block diagram is a high level modularization of the system that separates the overall system into maximally decoupled sub-systems. In each block of the diagram, the output and input are related together by a transfer function. The other supported languages are ladder logic, sequential function chart, structured text, and instruction list. Find the transfer function $$\frac{X(s)}{F(s)}$$ for the block diagram shown in the figure. How to Make a Block Diagram. In a closed loop control system, a fraction of output is fed-back and added to input of the system. It is possible to create such block diagrams and implement their … Next Page . In a block diagram, transfer functions of the system elements are represented by individual blocks. The block system is referred to in the UK as the method of working, in the US as the method of operation, and in Australia as safeworking. If we define the output of the first system as h(t), we can define h(t)as: 1. h ( t ) = x ( t ) ∗ f ( t ) {\displaystyle h(t)=x(t)… We are a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for us to earn fees by linking to Amazon.com and affiliated sites. Definitions. that is required for the system to be critically damped (ζ = 1). The following figure shows the block diagram of positive feedback control system. Where C(s) is the output and R(s) is the input of that particular block. We have studied several dynamic systems in previous chapters. pp 315-345 | Nowadays, PLC becomes more and more popular in industries for automation purpose. If we have two systems, f(t) and g(t), we can put them in series with one another so that the output of system f(t) is the input to system g(t). Previous Page. In the following system, it includes two blocks like controller as well as the controlled process. • Transfer functions, block diagrams and simplification • Feedback controllers • Control system design output input----- = fD() The general form x F---4 + D D2 ++4D 16 = -----An example. The open-loop control system block diagram is shown below. Basic Connections for Blocks. Here, resultant input signal is the summation of all input signals applied. Inputs and outputs, or signals, that flow to and from the system elements are represented by lines or arrows and their terminations define the manner in which different parts of the system interact. Consider the following block diagram model of a dynamic system where K Feedback Control System Block Diagram. By using visual illustration, even a very complex system can be simplified for the purpose of analysis. These keywords were added by machine and not by the authors. Consider a simple R-L circuit Apply KVL Now taking laplace transform of Eq.1 and Eq.2 with initial condition zero From eq.3 and eq.4 From fig: Now taking laplace transform of Eq.5, and Eq.6 For the right-hand side of eq.5, we will use a summing point. Each of them has its own transfer function. Engineers rely on the Simulink ® environment to build and simulate block diagrams for multidomain systems efficiently. Block … This process is experimental and the keywords may be updated as the learning algorithm improves. Full disclaimer here. Here it also to be remembered that the output of any block will not be affected by the presence of other blocks in the cascaded system. Block diagrams provide a Laplace domain, visual description that enables physically distinct systems to be represented using a common structure. In the figure below, there are two elements with transfer function Gone(s) and Gtwo(s). If same signal is applied to more than one system, then the signal is represented in the system by a point called take off point. Block diagrams of control systems are generally constructed according to structural, functional, or algorithmic design. Let us examine the shifting of summing point from a position before a block to a position after a block. Control systems are considered as one of the major aspects of our growing technology. It is not always convenient to derive the entire transfer function of a complex control system in a single function. While they have appeared to be physically distinct, we have seen that lumped parameter models of these mechanical, electrical, electromechanical, and thermal systems all exhibit the same fundamental behavior. Now, we can analyze them depending on whether we are using our classical or modern methods. 185.30.32.79. Next Page . Function Block Diagram is one of five languages for logic or control configuration supported by standard IEC 61131-3 for a control system such as a Programmable Logic Controller (PLC) or a Distributed Control System (DCS). Block: A Block (notation: rectangle with keyword = «block») represents a system component, a modular structural unit that encapsulates its contents (Properties, Behaviors, Constraints) and supports first-class (i.e., can be drawn and directly manipulated in the model repository) Interfaces. In the following diagram, the input can be given to the control system so that the required output can be obtained. Calculate the value of K It is easier and better to derive the transfer function of the control element connected to the system, separately. Block Diagram Representation of Control Systems By MSc. Signal Factor (inputs) pass through the design of the product and is output into measured Response Variable (also called the Ideal Function). Figure 4 shows basic elements of a feedback control system as represented by a block diagram. If Cone, Ctwo and Cthree are the outputs of the blocks with transfer function Gone, Gtwo and Gthree, then. Representation of a common input signal to more than one blocks of a control system is done by a common point as shown in the figure below with point X. the transfer function) to produce an effect resulting in controlled output or response. In other words – if there are more than one summing points directly inter associated, and then they can be easily interchanged from their position without affecting the final output of the summing system. The signal R(s) at take off point A will become G(s)R(s) at point B. • To be able to select controller parameters to m eet design objectives. It is not always convenient to derive the entire transfer function of a complex control system in a single function. So, such a complex diagram must be reduced to its simple or canonical form. This is a preview of subscription content, © Springer Science+Business Media New York 2015, University of North Carolina at Charlotte, https://doi.org/10.1007/978-1-4614-9293-1_10. Part of Springer Nature. Calculate the natural frequency, ω n , and damping ratio, ζ, for the plant. ("System block diagram" is the the more hardware-oriented term which emphasizes functionalities and intercommunications. The concepts discussed in the previous chapter are helpful for reducing (simplifying) the block diagrams. It cares less about what happens getting from input to output. Now let us examine the situation when take off point is shifted before the block which was previously after the block. Block diagrams derive their name from the rectangular elements found in this type of diagram. In addition to that, the diagram also shows there is a feedback path through which output signal C(s) is fed back and compared with the input R(s) and the difference between input and output is , which is acting as the actuating signal or error signal. When two or more systems are in series, they can be combined into a single representative system, with a transfer function that is the product of the individual systems. P- Diagram is essentially a schematic diagram that encompasses signal factor, control factor, noise factor and response variable. It is necessary to indicate the fine specifying the input signal entering a summing point in the block diagram of control system. If the proportional gain constant, K P , is equal to 20 and the commanded position is a step input x set = 3 ⋅ u(t), calculate the steady state error where the integral gain constant, K I , is equal to zero. But overall transfer function of the system is the ratio of transfer function of final output to transfer function of initial input of the system. Write a Matlab® script file that plots the response to a unit step input. Find the transfer functions for the following block diagrams. The following block diagram shows the closed loop dynamics of a positioning system consisting of a second-order plant, a feedback loop, and an actuator/amplifier with proportional integral gain. Over 10 million scientific documents at your fingertips. Block Diagram Reduction Rules. In other words, practical representation of a control system is its block diagram. In process control, block diagrams are a visual language for describing actions in a complex system in which blocks are black boxes that represent mathematical or logical operations that occur in sequence from left to right and top to bottom, but not the physical entities, such as processors or relays, that perform those operations. The control block diagram is a drawing that shows control connections and interfaces. Not logged in Follow these rules for simplifying (reducing) the block diagram, which is having many blocks, summing points and take-off points. Block diagrams consist of a single block or a combination of blocks. For (b) and (c), also calculate the damping ratio, ζ, and natural frequency, ω n . The output of the summing point is R(s) ± X(s). When several systems or control blocks are connected in cascaded manner, the transfer function of the entire system will be the product of transfer function of all individual blocks. For simplifying a complex control system, block diagrams are used. Hence another block of inverse of transfer function G(s) is to be put on that path to get R(s) again. The block diagram is to represent a control system in diagram form. What is Block Diagram A bock diagram is pictorial representation of the functions … The resultant signal is the input of a control system block of transfer function G(s) and the final output of the system is Write a Matlab ® script file that plots the response of the system to a unit step input. Electrical4U is dedicated to the teaching and sharing of all things related to electrical and electronics engineering. By combining the above two figures, we get the required block diagram. Cl… Write a Matlab® script file that plots the response to a step input F(t) = 20 ⋅ u(t). When a process is created (initialized or installed), the operating system creates a corresponding process control block. Department 2. Click here for a blank P-Diagram form in MS Excel. If you’re looking to do some control systems study, check out our control systems MCQs. block diagram: A block diagram is a visual representation of a system that uses simple, labeled blocks that represent single or multiple items, entities or concepts, connected by lines to show relationships between them. This principle is referred to as black box in engineering. The block diagram reduction process uses more time for complicated systems. When a train enters a block, signals at both ends change to indicate that the block is occupied, typically using red lamps or indicator flags. Instead of applying single input signal to different blocks as in the previous case, there may be such situation where different input signals are applied to same block. In other words, practical representation of a control system is its block diagram. Block diagrams give us a better understanding of a system’s functions and help create interconnections within it. At summing point, the input signal R(s) will be added to B(s) and produces actual input signal or error signal of the system and it is denoted by E(s). If the transfer function of input of control system is R(s) and the corresponding output is C(s), and the overall transfer function of the control system is G(s), then the control system can be represented as: When we need to apply one or the same input to more than one blocks, we use what’s known as the take off point. A block diagram is a graphical representation of a system – it provides a functional view of a system. In a block diagram, transfer functions of the system elements are represented by individual blocks. An important factor to remember is that the block diagram represents flowpaths of control signals, but does not represent flow of energy through the system or process. Block diagrams are used extensively to analyze control systems, where they provide a compact and intuitive representation of feedback control loops. Principle of shifting of take off point is that, it may be shifted either side of a block but final output of the branches connected to the take off point must be un-changed. The following figure shows the simple block diagram of a control system. A process control block (PCB) is a data structure used by computer operating systems to store all the information about a process.It is also known as a process descriptor.. For any control system, there exists a reference input known as excitation or cause which operates through a transfer operation (i.e. The The technique of combining of these blocks is referred to as block diagram reduction technique. • To be able to represent a control system with block diagrams. Advertisements. This algebra deals with the pictorial representation of algebraic equations. They are used to describe hardware and software systems as well as to represent processes. Normalerweise werden Blockdiagramme verwendet, um einen höheren Abstraktionsgrad zu bieten und somit ein besseres Verständnis der Funktion oder der Zusammenhänge des Systems zu ermöglichen. The reasons might be need to draw the (partially simplified) block diagram after each step. Block Diagram of a Control System. The above equation can be represented by a block of transfer function G(s) and input R(s) ± X(s)/G(s) again R(s)±X(s)/G(s) can be represented with a summing point of input signal R(s) and ± X(s)/G(s) and finally it can be drawn as below. There are two input signals R(s) and ± X(s) entering in a summing point at position A. What is a SysML Block Definition diagram? Block Diagram For Control Systems. Repeat part (d) when the integral gain constant, K I , is equal to 1. To overcome this you need use signal flow graphs (representation). In the above block diagrams of control system output can be rewritten as Since, the output is controlled by varying input, the control system got this name. 1. We will vary this input with some mechanism. Ein Blockdiagramm (auch Blockbild oder Blockschema) ist ein meist 2-dimensionales, grafisches Diagramm eines mechanisch-elektrischen Systems oder eines Berechnungsschemas, mit dessen Hilfe die Funktion des Systems beschrieben werden kann. A summing point with more than two inputs can be divided into two or more consecutive summing points, where alteration of the position of consecutive summing points does not affect the output of the signal. Calculate the transfer function $$\frac{X(s)}{F(s)}$$ in terms of the feedback parameter K. For the case where K = 0 and the input, f(t), is a unit delta function, δ(t), calculate x(t) using Laplace transforms. A complex control system consists of several blocks. The block diagram representation of a system is nothing but an interconnection of multiple elements of the system. Where, G(s) is the overall transfer function of cascaded control system. Here the output of summing point is given to the block, and the output of the block is I(s) Now the output I(s) is given to another block containing element SL and the output of this block is V0. (Supervisory Control and Data Acquisition), Programmable Logic Controllers (PLCs): Basics, Types & Applications, Diode: Definition, Symbol, and Types of Diodes, Thermistor: Definition, Uses & How They Work, Half Wave Rectifier Circuit Diagram & Working Principle, Lenz’s Law of Electromagnetic Induction: Definition & Formula. Each element of the control system is represented with a block and the block is the symbolic representation of the transfer function of that element. Calculate x(t) using Laplace transforms if F(t) = δ(t) and K = 0 and, then, K = 10. is a constant feedback parameter. In this article, we focus on the first definition. Find the transfer function $$\frac{X(s)}{F(s)}$$ for the block diagram shown in the figure. Basically block diagram of a control system pictorially represents a system. For software engineering, some will call this sort of diagram a "software block diagram" or simply a "block diagram".) This service is more advanced with JavaScript available, System Dynamics for Mechanical Engineers For successful implementation of this technique, some rules for block diagram reduction to be followed. Block diagram representing flight control system of an aircraft. Main and secondary control rooms may be defined with a specific hierarchy. Block diagrams provide a Laplace domain, visual description that enables physically distinct systems to be represented using a common structure. Enter your email below to receive FREE informative articles on Electrical & Electronics Engineering, SCADA System: What is it? Cite as. This overall transfer function of the system can be obtained by simplifying the control system by combining this individual blocks, one by one. However, when we deal with control systems, then we come across various complex block diagram representation of systems that holds various functional blocks with multiple summing points and take-off points. Previous Page. Find the tranfer function $$\frac{X(s)}{F(s)}$$ for the block diagram shown in the figure.
2020 what is block diagram in control system
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2021-03-08 06:35:53
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https://nforum.ncatlab.org/discussion/10314/dependent-sum-type/
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• CommentRowNumber1.
• CommentAuthorGuiGeek
• CommentTimeSep 12th 2019
In the page dependent sum type, the presented “term introduction rule” seems not really dependent, since the typing derivation of the second element is not aware of the first. I would expect $\frac{\vdash t:A\quad \vdash u:B[t/x]}{\vdash (t,u):\Sigma(x:A).B}$ which corresponds to what is presented in the text on positive and negative versions.
• CommentRowNumber2.
• CommentAuthoratmacen
• CommentTimeSep 12th 2019
• (edited Sep 12th 2019)
I guess they meant
$\frac{x:X \vdash a:A(x)}{x:X \vdash (x,a) : \sum_{x':X}A(x')}$
which I think is basically the right idea. But that’s not the usual rule either, since it doesn’t allow you to construct pairs in the empty context, unless you have a primitive substitution rule.
So the usual rule uses an arbitrary term of $X$:
$\frac{t:X \qquad a:A(t)}{(t,a) : \sum_{x:X}A(x)}$
This is the same as what you wrote, but with different notation.
• CommentRowNumber3.
• CommentAuthorGuiGeek
• CommentTimeSep 12th 2019
But what they meant looks wrong to me, since it does not allow to introduce any pair which first element is not a variable, for instance to prove $(0,Nil):\Sigma(n:Nat).Vect\,n$.
• CommentRowNumber4.
• CommentAuthoratmacen
• CommentTimeSep 12th 2019
Right, that’s why you’d need a substitution rule:
$\frac{\Gamma \vdash a\,:\,A \qquad \Gamma,x:A,\Gamma' \vdash t\,:\,T}{\Gamma,\Gamma'[a/x] \vdash t[a/x]\,:\,T[a/x]}$
So combining this with the variables-only pairing rule ($\Gamma' \coloneqq \cdot$, $a \coloneqq t$, $A \coloneqq X$, $t \coloneqq (x,a)$, $T \coloneqq \sum_{x':X}A(x')$) we get:
$\frac{\Gamma \vdash t\,:\,X \qquad \Gamma,x:X \vdash (x,a)\,:\,\sum_{x':X}A(x')}{\Gamma \vdash (t,a[t/x])\,:\,\sum_{x':X}A(x')}$
This is sufficiently general, since $x$ need not be free in $a$. (And there’s actually no reason for $x$ to be free in $a$ when you just immediately substitute, since both $t$ and $a$ are provided together. What you really want is for $x$ to be free in $A(x)$, of course.)
• CommentRowNumber5.
• CommentAuthorMike Shulman
• CommentTimeSep 12th 2019
I think we should give the usual rule, as in #2. Anyone who wants to fix it, please do!
• CommentRowNumber6.
• CommentAuthoratmacen
• CommentTimeSep 12th 2019
Now I’m not sure anymore. The argument I gave justifies:
$\frac{t:X \qquad x:X \vdash a\,:\,A(x)}{(t,a[t/x])\,:\,\sum_{x':X}A(x')}$
But having to prove $A(x)$ generically, rather than just $A(t)$ sounds harder, so maybe the rule is still too weak? Oh right, I guess it must be: what if $X$ is $bool$ and $A(x)$ is $\{true \mapsto \top,\;false \mapsto \bot\}$?
Yeah OK, it looks like requiring a variable was a red herring; the problem was that the premise isn’t depending on a specific term, like GuiGeek originally said.
• CommentRowNumber7.
• CommentAuthoratmacen
• CommentTimeSep 12th 2019
So the diagram next to the bad intro rule seems misleading: that $x$ arrow doesn’t have to be a context projection.
• CommentRowNumber8.
• CommentAuthoratmacen
• CommentTimeSep 12th 2019
Re #5: I edited the table include. Fixed?
• CommentRowNumber9.
• CommentAuthorMike Shulman
• CommentTimeSep 12th 2019
Yes, looks good. Thanks for catching this, GuiGeek, and for fixing it, Matt!
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2019-10-23 02:04:01
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http://www.proofwiki.org/wiki/Multiplicity_of_Prime_Factor_in_Factorial
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# Multiplicity of Prime Factor in Factorial
## Theorem
Let $n!$ be the factorial of $n$.
Let $p$ be a prime number.
Then $p^\mu$ is a divisor of $n!$, and $p^{\mu + 1}$ is not, where:
$\displaystyle \mu = \sum_{k \mathop > 0} \left \lfloor{\frac n {p^k}}\right \rfloor$
where $\left \lfloor{\cdot}\right \rfloor$ denotes the Floor Function.
## Proof
Note that although the summation given in the statement of the theorem is given as an infinite sum, in fact it terminates after a finite number of terms (because when $p^k > n$ we have $0 < n/p^k < 1$).
From Number of Multiples Less Than a Given Number, we have that $\left \lfloor{\dfrac n {p^k}}\right \rfloor$ is the number of integers $m$ such that $0 < m \le n$ which are multiples of $p^k$.
We look more closely at $n!$:
$n! = 1 \times 2 \times \ldots \times \left({n-1}\right) \times n$
We see that any integer $m$ such that $0 < m \le n$ which is divisible by $p^j$ and not $p^{j+1}$ must be counted exactly $j$ times.
That is: once in $\left \lfloor{\dfrac n p}\right \rfloor$, once in $\left \lfloor{\dfrac n {p^2}}\right \rfloor$, $\ldots$, once in $\left \lfloor{\dfrac n {p^j}}\right \rfloor$.
And that is all the occurrences of $p$ as a factor of $n!$.
Thus:
$\displaystyle \mu = \left \lfloor{\frac n p}\right \rfloor + \left \lfloor{\frac n {p^2}}\right \rfloor + \cdots + \left \lfloor{\frac n {p^j}}\right \rfloor$
Hence the result.
$\blacksquare$
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2013-12-13 07:46:41
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http://www.r-bloggers.com/page/480/
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## Sweave Tutorial 3: Console Input and Output – Multiple Choice Test Analysis
November 30, 2010
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This post provides an example of using Sweave to perform an item analysis of a multiple choice test. It is designed as a tutorial for learning more about using Sweave in a mode where console input and output is displayed. Copies of all source code a...
## Sweave Tutorial 3: Console Input and Output – Multiple Choice Test Analysis
November 30, 2010
By
This post provides an example of using Sweave to perform an item analysis of a multiple choice test. It is designed as a tutorial for learning more about using Sweave in a mode where console input and output is displayed. Copies of all source code a...
## Hägerstrand Time-Space Cube
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With the rgl package it’s possible to interact with the 3d visualization of the timespace tracks. Code example: plot3d(lon,lat,timedate, xlim=range(lon), ylim=range(lat), zlim=range(timedate), ticktype=”detailed”, xlab=”longitude”, ylab=”latitude”, zlab=”Date”, col= as.POSIXlt(daten)\$mday, type=”l”, main=plottitle) In the posted example individual waypoints were added by drawing vertical lines.
November 30, 2010
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I started to develop GOSemSim package two years ago when I was not quite familiar with R. I am very happy to see that someone use it and found it helpful. I try to learn S4 and redesign GOSemSim with S4 classes and methods in the pass two weeks, and the very first version was implemented. As I’m not...
November 30, 2010
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I started to develop GOSemSim package two years ago when I was not quite familiar with R. I am very happy to see that someone use it and found it helpful. I try to learn S4 and redesign GOSemSim with S4 classes and methods in the pass two weeks, and the very first version was implemented. As I’m...
## Analysis of retractions in PubMed
November 30, 2010
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As so often happens these days, a brief post at FriendFeed got me thinking about data analysis. Entitled “So how many retractions are there every year, anyway?”, the post links to this article at Retraction Watch. It discusses ways to estimate the number of retractions and in particular, a recent article in the Journal of
## Data visualization videos
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## Initializing the Holt-Winters method
November 29, 2010
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The Holt-Winters method is a popular and effective approach to forecasting seasonal time series. But different implementations will give different forecasts, depending on how the method is initialized and how the smoothing parameters are selected. In this post I will discuss various initialization methods. Suppose the time series is denoted by and the seasonal period
## Sorting out Sweave in Eclipse/StatET
November 29, 2010
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Using Sweave to produce pretty-looking documentation for R is awfully handy. It takes a little tweaking to get set up in Eclipse and StatET though. I followed the information in Jeromy Anglim’s webpage to originally get Sweave set up. The followi...
## Slices and crumbs [arXiv:1011.4722]
November 29, 2010
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$Slices and crumbs [arXiv:1011.4722]$
An interesting note was arXived a few days ago by Madeleine Thompson and Radford Neal. Beside the nice touch of mixing crumbs and slices, the neat idea is to have multiple-try proposals for simulating within a slice and to decrease the dimension of the simulation space at each try. This dimension diminution is achieved via
## The Joy of Visualizations
November 29, 2010
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This is a clip from the forthcoming BBC4 program, The Joy of Stats: The clip shows Hans Rosling (who we've profiled here before), plotting life expectancy versus income for various countries, and animating over time. The clip amply demonstrates that with the right presentation and story, even the simplest of scatterplots can be a joy to behold. I'm looking...
## Altering Eclipse user name
November 29, 2010
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Using StatET’s code generation templates is handy, but the standard Eclipse variable for \${user} just inserts the currently logged-in user’s account name. If you want a different name to appear when \${user} is called, one method is to alter...
## John Chambers on R and Multilingualism
November 29, 2010
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John Chambers, one of the creators of R's predecessor S and a current member of the R Core Group, gave a seminar at Stanford last week titled "R, other languages and object-oriented programming". Unfortunately, I was away for the Thanksgiving break and couldn't make it myself, but John has kindly made his slides (PDF) available for download. The talk...
## John Chambers on R and Multilingualism
November 29, 2010
By
John Chambers, one of the creators of R's predecessor S and a current member of the R Core Group, gave a seminar at Stanford last week titled "R, other languages and object-oriented programming". Unfortunately, I was away for the Thanksgiving break and couldn't make it myself, but John has kindly made his slides (PDF) available for download. The talk...
## Statistique de l’assurance STT6705V, partie 11
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## SAS and R joins SAS-x
November 29, 2010
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Tal Galili, organizer of the R-bloggers blog aggregator, has opened a new aggregator for people blogging about SAS. If you're unfamiliar with the concept, an aggregator is a single blog which republishes (with permission, in this case) the entries fro...
## INFORMS Data Mining Competition leaders used Open Source software
November 29, 2010
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The results of 2010 INFORMS data mining competition just recently finished. The leaders were presented at the 2010 Annual INFORMS Conference. The 2010 INFORMS data mining competition goal was to determine short term movements in stock price...
## INFORMS Data Mining Competition leaders used Open Source software
November 29, 2010
By
The results of 2010 INFORMS data mining competition just recently finished. The leaders were presented at the 2010 Annual INFORMS Conference. The 2010 INFORMS data mining competition goal was to determine short term movements in stock price...
## Joy of Stats coming soon
November 29, 2010
By
The Joy of Stats really is a joy. It will be shown on BBC4, apparently scheduled for December 7. (That date comes from Hans Rosling on twitter, I haven’t found scheduling evidence at the BBC.) I saw its debut at the Royal Statistical Society on World Statistics Day. Here is a five minute excerpt: You … Continue reading...
## Sweave Tutorial 2: Batch Individual Personality Reports using R, Sweave, and LaTeX
November 29, 2010
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This post documents an example of using Sweave to generate individualised personality reports based on responses to a personality test. Each report provides information on both the responses of the general sample and responses of the specific respond...
## Sweave Tutorial 2: Batch Individual Personality Reports using R, Sweave, and LaTeX
November 29, 2010
By
This post documents an example of using Sweave to generate individualised personality reports based on responses to a personality test. Each report provides information on both the responses of the general sample and responses of the specific respond...
## Getting Started with Git, EGit, Eclipse, and GitHub: Version Control for R Projects
November 28, 2010
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## Getting Started with Git, EGit, Eclipse, and GitHub: Version Control for R Projects
November 28, 2010
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## Computing evidence
November 28, 2010
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The book Random effects and latent variable model selection, edited by David Dunson in 2008 as a Springer Lecture Note. contains several chapters dealing with evidence approximation in mixed effect models. (Incidentally, I would be interested in the story behind the Lecture Note as I found no explanation in the backcover or in the preface.
## Analyst First – SURF
November 28, 2010
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This presentation is aimed at all those working in commercial and government analytics, irrespective of what tools they use, and also to those students intending on such a career. R and other open source tools play a powerful, unique and … Continue reading →
## Random variable generation (Pt 1 of 3)
November 28, 2010
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$Random variable generation (Pt 1 of 3)$
As I mentioned in a recent post, I’ve just received a copy of Advanced Markov Chain Monte Carlo Methods. Chapter 1.4 in the book (very quickly) covers random variable generation. Inverse CDF Method A standard algorithm for generating random numbers is the inverse cdf method. The continuous version of the algorithm is as follows: 1.
## parser 0.0-12
November 28, 2010
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I've pushed a new version of the parser package to CRAN. This is the first release that depends on Rcpp, which allowed me to reduce the code size and increase its maintainability. This also features a faster version of nlines, a function that r...
## Rcpp 0.8.9
November 28, 2010
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Rcpp 0.8.9 was pushed to CRAN recently. Apart from minor bug fixes, this release concentrates on modules, with lots of new features to expose C++ functions and classes through R reference classes. The Rcpp-modules vignette has all the details, a...
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2015-04-18 08:53:33
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http://jeannicod.ccsd.cnrs.fr/ijn_00000057
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Towards a Science of Consciousness (2002)
Liste des fichiers attachés à ce document :
PDF
ijn_00000057_00.pdf(110.8 KB)
Qualia Domesticated
(2002)
Consider the following argument (1) If panpsychism is true, then the hard problem of consciousness is solved (2) Physicalism is true (3) Physicalism entails panpsychism. We conclude that (4) The hard problem of consciousness is solved. This is a valid argument, and one whose conclusion has a certain appeal. What about the premisses? How exactly is panpsychism a solution to the problem of phenomenal consciousness? Who can take panpsychism seriously, and how can panpsychism be entailed by physicalism? A little forcing is assumed in suggesting to consider a philosophical argument whose conclusion is panpsychism. But I think the exercise is worthwhile, provided we spell out all the consequences of forcing.
Thématiques scientifiques : Sciences de l'Homme et Société/Philosophie/Philosophie de l'esprit
Mots-clés : qualia – physicalism
ijn_00000057, version 1 http://jeannicod.ccsd.cnrs.fr/ijn_00000057 oai:jeannicod.ccsd.cnrs.fr:ijn_00000057 Contributeur : Roberto Casati <> Soumis le : Mardi 25 Juin 2002, 13:24:51 Dernière modification le : Mardi 25 Juin 2002, 13:24:51
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2014-07-24 04:13:04
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https://www.physicsforums.com/threads/second-diff-eq-question-of-the-day.290909/
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# Second Diff Eq question of the day
1. Feb 8, 2009
1. The problem statement, all variables and given/known data
10. If y(t) = -te^(3t) is a solution to y'' + py' + qy = 0, then what are p and q?
2. Relevant equations
3. The attempt at a solution
so it's equal to r^2 + pr +q = 0, but then how can i find the two numbers?
thanks
2. Feb 8, 2009
### rootX
You don't need to do any algebra. Remember there are some formulas for solving different equations? This one looks like e^at (At + B) form. Just look over them.
3. Feb 8, 2009
### Staff: Mentor
If your solutions were y1 = e^(3t) and y2 = e^(4t), your characteristic equation would be r^2 - 7r + 12 = 0, or (r - 3)(r - 4) = 0, right?
Under what circumstances related to the work above will you get a solution y = te^(3t)?
4. Feb 9, 2009
### HallsofIvy
Staff Emeritus
You don't need to look at the characteristic equation at all. If $y= -te^{3t}$ then $y'= -e^{3t}- 3te^{3t}= -(1+ 3t)e^{3t}$ and y"= $-3e^{3t}- 3(1+ 3t)e^{3t}$$= -(6+ 9t)e^{3t}$. Putting those into the equation we have $-(6+ 9t)e^{3t}- p(1+ 3t)e^{3t}- qte^{3t}= ((-6- p)+(-9-3p-q)t)e^{3t}= 0$ for all t. Since $e^{3t}$ is never 0, we must have (-6- p)+ (-9-3p-q)t= 0 for all t which means we must have -6-p= 0 and -9- 3p- q= 0.
Of course, it is also true that eat will be a solution if and only if a is a root of the characteristic equation and that teat will be a solution if and only if a is a double root of the characteristic equation, which means that the characteristic equation must reduce to (x-a)2= 0.
Last edited: Feb 9, 2009
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2017-08-19 23:28:02
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http://vincentverheyen.com/filter/tips
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# Compose tips
• You can insert footnotes directly into texts with [fn]This text becomes a footnote.[/fn]. This will be replaced with a running number (the footnote reference) and the text within the [fn] tags will be moved to the bottom of the page (the footnote). See <a href="http://drupal.org/project/footnotes">Footnotes Readme page</a> for additional usage options.
• Mathematics inside the configured delimiters is rendered by MathJax. The default math delimiters are $$...$$ and $...$ for displayed mathematics, and $...$ and $...$ for in-line mathematics.
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2021-10-20 07:25:12
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http://math.stackexchange.com/questions/116042/finding-the-component-of-a-vector-tangent-to-a-circle
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# Finding the component of a vector tangent to a circle
## Problem
Given a vector and a circle in a plane, I'm trying to find the component of the vector that is tangent to the circle. The location of the tangent vector is unimportant; I only need to know its magnitude and whether it is directed clockwise or counter clockwise about the circle.
## Background (just in case you're interested)
I'm writing an iPhone app that displays a dial. The user is allowed to spin the dial by dragging it around with his finger. If the user then flicks his finger in some direction (and lets go), the dial should continue to spin before coming to a stop. For added realism, the amount of spin should be directly proportional to the velocity of the flick. In other words, I'm simulating the inertia and momentum of the dial.
The OS already provides a vector describing the velocity and direction of the flick. Note that if it happened to be tangential to the dial, I could simply find the magnitude of the vector and use it directly as the amount of spin. But the flick could be in any direction -- even outside the dial. A flick along the radius of the dial, for example, should result in no motion. Therefore, I need to find:
1. The component of the flick vector that is tangential to the dial
2. Whether this tangent vector is clockwise or counter clockwise around the dial
With this information, I can calculate how much spin should be put on the dial by finding the magnitude of the tangent vector.
## Illustration
That might not be clear, so here's a diagram to illustrate:
• $V$: flick vector
• $P$: start point of the vector
• $D$: midpoint of the vector
• $T$: tangent vector I'm trying to find
• $E$: point where the tangent vector touches the circle
• $R$: radius of the circle
• $C$: center of the circle
• $T'$: another way of looking at the tangent vector (for an alternate approach described later)
• $V_{2}$, $V_{3}$: other possible flick vectors
## My approach
My first approach was to derive an equation for the tangent line ($T$).
The midpoint $D$ would be given by:
$D = ( P_{x} + \frac{V_{x}}{2}, P_{y} + \frac{V_{y}}{2})$
The slope $m$ of line $\overline{C D}$ would be:
$m = \frac{D_{y} - C_{y}}{D_{x} - C_{x}} = \frac{P_{y}+\frac{V_{y}}{2} - C_{y}}{P_{x} + \frac{V_{x}}{2} - C_{x}}$
And then the equation for line $\overline{C D}$ would be:
$y - C_{y} = m(x - C_{x})$
$E$ would be the intersection of that line and the circle:
$(x - C_{x})^{2} + (y - C_{y})^{2} = R^{2}$
By solving for $x$ and $y$ in the $\overline{C D}$ equation and substituting into the circle equation, I get:
$x = C_{x} ± \frac{R}{\sqrt{1 + m^{2}}}$
$y = C_{y} ± \frac{R}{\sqrt{1 + m^{2}}}$
These $x, y$ values are the coordinates of point $E$.
Now I finally have an equation for the tangent line $T$. I simply use the perpendicular slope of line $\overline{C D}$ and the coordinates of point $E$:
$y - E_{y} = - \frac{1}{m}(x - E_{x})$
I've verified that my work is correct by plugging in some numbers, but I'm not sure what to do next. I still don't have the magnitude of the tangent vector.
## Alternate approach
As an alternate approach, I thought of ignoring $T$ altogether and considering $T'$ instead, since I only need to know the magnitude of the tangent vector. But in the right triangle I only know the length of the hypotenuse ($|V|$). That's not enough information to determine the length of $T'$.
Or, if I could somehow determine the $x, y$ components of $T'$, then I believe the dot product ($V \cdot T'$) would give me the magnitude of the tangential component of the vector V. (Please correct me if I'm wrong.) But I'm not sure how to get those values in the first place.
How can I proceed? Thanks for any suggestions.
-
The vector $T$ is the component of $V$ perpendicular to $CD$. Assuming the center of the circle $C$ is the origin, this is just $$T = V - \frac{D(D\cdot V)}{\lVert D\rVert^2}.$$
If you want the signed magnitude of the vector, with positive being anticlockwise and negative being clockwise, you should take the cross product of $D/\lVert D\rVert$ and $V$ instead. In two dimensions, the cross product of two vectors is a scalar, $$u \times v = \begin{vmatrix}u_x & v_x \\ u_y & v_y\end{vmatrix} = u_xv_y - u_yv_x.$$
If the circle is not centered at the origin, just replace $D$ with $D - C$ in all of the above expressions.
-
Thanks for your answer! When you say $D$, I assume you mean the vector from C to D. I applied your formula for $T$ and I seem to be getting the correct values back. However, I'm not understanding your technique for getting the circular direction. I thought the cross product is always a vector, not a scalar. In any case, I applied your function and got a negative value for V (clockwise -- correct) but also a negative value for $V_{2}$ (clockwise -- incorrect). Any thoughts? Thanks. – vocaro Mar 5 '12 at 6:19
Strictly speaking, the cross product is a function from pairs of 3D vectors to 3D vectors, but if you have two 2D vectors $\vec u$ and $\vec v$, the cross product of $(u_x, u_y, 0)$ and $(v_x, v_y, 0)$ is the vector $(0, 0, w)$ where $w = u_xv_y - u_yv_x$, so one can think of $w$ as "the cross product in 2D" of $\vec u$ and $\vec v$. I don't know if it has a more specific name, but it is a fairly natural thing to do. From the picture, I don't think the value for $\vec V_2$ should be negative. Can you tell me the coordinates of $\overrightarrow{CD}$ and $V$ in that case? – Rahul Mar 5 '12 at 17:04
Sorry, my calculations were wrong. $V_{2}$ is indeed positive as you predicted. I have accepted your answer; thank you for your help! – vocaro Mar 6 '12 at 5:25
I think that the simplest way would be like this:
Firstly, find the angle between (the line from the center of the circle to the midpoint of the Vector) and (the Vector itself). (Do you know how to do this? If not, comment and we can expand). I'm capitalizing the V in the Vector we start with to distinguish it.
Once you have this angle $\theta$, then the length of the tangent you're looking for is given by $L\sin^{} \theta$, where $L$ is the length of the Vector. And whether it's clockwise or counterclockwise should come from your calculation of the angle.
Or we could do everything with complex numbers. If the angle that the midpoint-line makes with the positive real axis is $\theta$, then multiply the complex representatives of the endpoints of the Vector by $e^{-i\theta}$, and calculate the imaginary part of the difference $d$ between the endpoints. Then positive and negative correspond to positive and negative imaginary part, respectively. And for that matter, the tangent vector is given by $e^{i \theta} \text{Im}(d)$, where Im stands for the imaginary part.
If you know some complex, then you'll see we rotated the vector so that our tangent point on the circle is always $(1,0)$, so we took the $y$ component and rotated it back.
-
Thanks for your answer! Unfortunately I'm not sure which angle you're calling θ. Do you mean CDP or CPD? I can compute either one using the dot product formula, but after that I'm not sure what to do. For example, I plugged in numbers and got 1.3 radians (75 degrees) for angle CDP, which looks right. But I can't plug this value into your $Lsin^{-1}θ$ formula because the inverse sine only allows values from -1 to 1. By the way, what formula is that? How was it derived? Thanks. – vocaro Mar 4 '12 at 4:09
@Vocaro: Whoops! I didn't mean to include the inverse part of the inverse sine. That was a terrible mistake, and of course you shouldn't get any real value for that part. I just meant to refer to the triangle, that's all. – mixedmath Mar 4 '12 at 6:05
Thanks for the correction. When I apply the dot product formula to find the angle CDP, it looks correct, and when I apply $Lsinθ$, the tangent length looks correct also. However, you said "whether it's clockwise or counterclockwise should come from your calculation of the angle." The dot product formula I'm using is $arccos(\frac{A_{x}B_{x}+A_{y}B_{y}}{|A||B|})$, which will always give a positive angle. Am I using the right formula here? – vocaro Mar 4 '12 at 20:03
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2014-03-13 19:59:44
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https://en.wikipedia.org/wiki/Fast_inverse_square_root
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# Fast inverse square root
Lighting and reflection calculations, as in the video game OpenArena, use the fast inverse square root code to compute angles of incidence and reflection.
Fast inverse square root, sometimes referred to as Fast InvSqrt() or by the hexadecimal constant 0x5F3759DF, is an algorithm that estimates ${\displaystyle {\frac {1}{\sqrt {x}}}}$, the reciprocal (or multiplicative inverse) of the square root of a 32-bit floating-point number ${\displaystyle x}$ in IEEE 754 floating-point format. This operation is used in digital signal processing to normalize a vector, such as scaling it to length 1. For example, computer graphics programs use inverse square roots to compute angles of incidence and reflection for lighting and shading. Predated by similar video game algorithms, this one is best known for its implementation in 1999 in Quake III Arena, a first-person shooter video game heavily based on 3D graphics. The algorithm only started appearing on public forums between 2002 and 2003.[note 1] Computation of square roots usually depends upon many division operations, which for floating point numbers are computationally expensive. The fast inverse square generates a good approximation with only one division step.
The algorithm accepts a 32-bit floating-point number as the input and stores a halved value for later use. Then, treating the bits representing the floating-point number as a 32-bit integer, a logical shift right by one bit is performed and the result subtracted from the number 0x5F3759DF (in decimal notation: 1,597,463,007), which is a floating-point representation of an approximation of ${\displaystyle {\sqrt {2^{127}}}}$.[2] This results in the first approximation of the inverse square root of the input. Treating the bits again as a floating-point number, it runs one iteration of Newton's method, yielding a more precise approximation.
The algorithm was often misattributed to John Carmack, but in fact the code is based on an unpublished paper by William Kahan and K.C. Ng circulated in May 1986. The original constant was produced from a collaboration between Cleve Moler and Gregory Walsh, while they worked for Ardent Computing in the late 1980s.
With subsequent hardware advancements, especially the x86 SSE instruction rsqrtss, this method is not generally applicable to general purpose computing,[3] though it remains an interesting example both historically[4] and for more limited machines, such as low-cost embedded systems. However, more manufacturers of embedded systems are including trigonometric and other math accelerators such as CORDIC, avoiding the need for such algorithms.
## Motivation
Surface normals are used extensively in lighting and shading calculations, requiring the calculation of norms for vectors. A field of vectors normal to a surface is shown here.
A two-dimensional example of using the normal ${\displaystyle C}$ to find the angle of reflection from the angle of incidence; in this case, on light reflecting from a curved mirror. The fast inverse square root is used to generalize this calculation to three-dimensional space.
The inverse square root of a floating point number is used in calculating a normalized vector.[5] Programs can use normalized vectors to determine angles of incidence and reflection. 3D graphics programs must perform millions of these calculations every second to simulate lighting. When the code was developed in the early 1990s, most floating point processing power lagged the speed of integer processing.[6] This was troublesome for 3D graphics programs before the advent of specialized hardware to handle transform and lighting.
The length of the vector is determined by calculating its Euclidean norm: the square root of the sum of squares of the vector components. When each component of the vector is divided by that length, the new vector will be a unit vector pointing in the same direction. In a 3D graphics program, all vectors are in three-dimensional space, so ${\displaystyle {\boldsymbol {v}}}$ would be a vector ${\displaystyle (v_{1},v_{2},v_{3})}$.
${\displaystyle \|{\boldsymbol {v}}\|={\sqrt {v_{1}^{2}+v_{2}^{2}+v_{3}^{2}}}}$
is the Euclidean norm of the vector.
${\displaystyle {\boldsymbol {\hat {v}}}={\frac {\boldsymbol {v}}{\left\|{\boldsymbol {v}}\right\|}}}$
is the normalized (unit) vector, using ${\displaystyle \|{\boldsymbol {v}}\|^{2}}$ to represent ${\displaystyle v_{1}^{2}+v_{2}^{2}+v_{3}^{2}}$.
${\displaystyle {\boldsymbol {\hat {v}}}={\frac {\boldsymbol {v}}{\sqrt {\left\|{\boldsymbol {v}}\right\|^{2}}}}}$
which relates the unit vector to the inverse square root of the distance components. The inverse square root can be used to compute ${\displaystyle {\boldsymbol {\hat {v}}}}$ because this equation is equivalent to
${\displaystyle {\boldsymbol {\hat {v}}}={\boldsymbol {v}}\,{\frac {1}{\sqrt {\left\|{\boldsymbol {v}}\right\|^{2}}}}}$
where the fraction term is the inverse square root of ${\displaystyle \|{\boldsymbol {v}}\|^{2}}$.
At the time, floating-point division was generally expensive compared to multiplication; the fast inverse square root algorithm bypassed the division step, giving it its performance advantage.
## Overview of the code
The following code is the fast inverse square root implementation from Quake III Arena, stripped of C preprocessor directives, but including the exact original comment text:[7]
float Q_rsqrt( float number )
{
long i;
float x2, y;
const float threehalfs = 1.5F;
x2 = number * 0.5F;
y = number;
i = * ( long * ) &y; // evil floating point bit level hacking
i = 0x5f3759df - ( i >> 1 ); // what the fuck?
y = * ( float * ) &i;
y = y * ( threehalfs - ( x2 * y * y ) ); // 1st iteration
// y = y * ( threehalfs - ( x2 * y * y ) ); // 2nd iteration, this can be removed
return y;
}
At the time, the general method to compute the inverse square root was to calculate an approximation for ${\displaystyle {\frac {1}{\sqrt {x}}}}$, then revise that approximation via another method until it came within an acceptable error range of the actual result. Common software methods in the early 1990s drew approximations from a lookup table.[8] The key of the fast inverse square root was to directly compute an approximation by utilizing the structure of floating-point numbers, proving faster than table lookups. The algorithm was approximately four times faster than computing the square root with another method and calculating the reciprocal via floating-point division.[9] The algorithm was designed with the IEEE 754-1985 32-bit floating-point specification in mind, but investigation from Chris Lomont showed that it could be implemented in other floating-point specifications.[10]
The advantages in speed offered by the fast inverse square root trick came from treating the 32-bit floating-point word[note 2] as an integer, then subtracting it from a "magic" constant, 0x5F3759DF.[6][11][12][13] This integer subtraction and bit shift results in a bit pattern which, when re-defined as a floating-point number, is a rough approximation for the inverse square root of the number. One iteration of Newton's method is performed to gain some accuracy, and the code is finished. The algorithm generates reasonably accurate results using a unique first approximation for Newton's method; however, it is much slower and less accurate than using the SSE instruction rsqrtss on x86 processors also released in 1999.[3][14]
### Worked example
As an example, the number ${\displaystyle x=0.15625}$ can be used to calculate ${\displaystyle {\frac {1}{\sqrt {x}}}\approx 2.52982}$. The first steps of the algorithm are illustrated below:
0011_1110_0010_0000_0000_0000_0000_0000 Bit pattern of both x and i
0001_1111_0001_0000_0000_0000_0000_0000 Shift right one position: (i >> 1)
0101_1111_0011_0111_0101_1001_1101_1111 The magic number 0x5F3759DF
0100_0000_0010_0111_0101_1001_1101_1111 The result of 0x5F3759DF - (i >> 1)
Interpreting as IEEE 32-bit representation:
0_01111100_01000000000000000000000 1.25 × 2−3
0_00111110_00100000000000000000000 1.125 × 2−65
0_10111110_01101110101100111011111 1.432430... × 263
0_10000000_01001110101100111011111 1.307430... × 21
Reinterpreting this last bit pattern as a floating point number gives the approximation ${\displaystyle y=2.61486}$, which has an error of about 3.4%. After one single iteration of Newton's method, the final result is ${\displaystyle y=2.52549}$, an error of only 0.17%.
### Avoiding undefined behavior
According to the C standard, reinterpreting a floating point value as an integer by removing the pointer to it is considered unexpected behavior (undefined behavior). Another way would be to place the floating point value in an anonymous union containing an additional 32-bit unsigned integer member, and accesses to that integer provides a bit level view of the contents of the floating point value. However, type punning through a union is also undefined behavior in C++.
#include <stdint.h> // uint32_t
float Q_rsqrt(float number)
{
union {
float f;
uint32_t i;
} conv = { .f = number };
conv.i = 0x5f3759df - (conv.i >> 1);
conv.f *= 1.5F - (number * 0.5F * conv.f * conv.f);
return conv.f;
}
In C++ the usual method for implementing this function's casts is through C++20's std::bit_cast. This also allows the function to work in constexpr context:
#include <bit>
#include <limits>
#include <cstdint>
constexpr float Q_rsqrt(float number) noexcept
{
static_assert(std::numeric_limits<float>::is_iec559); // (enable only on IEEE 754)
float const y = std::bit_cast<float>(
0x5f3759df - (std::bit_cast<std::uint32_t>(number) >> 1));
return y * (1.5f - (number * 0.5f * y * y));
}
## Algorithm
The algorithm computes ${\displaystyle {\frac {1}{\sqrt {x}}}}$ by performing the following steps:
1. Alias the argument ${\displaystyle x}$ to an integer as a way to compute an approximation of the binary logarithm ${\displaystyle \log _{2}(x)}$
2. Use this approximation to compute an approximation of ${\displaystyle \log _{2}\left({\frac {1}{\sqrt {x}}}\right)=-{\frac {1}{2}}\log _{2}(x)}$
3. Alias back to a float, as a way to compute an approximation of the base-2 exponential
4. Refine the approximation using a single iteration of Newton's method.
### Floating-point representation
Since this algorithm relies heavily on the bit-level representation of single-precision floating-point numbers, a short overview of this representation is provided here. To encode a non-zero real number ${\displaystyle x}$ as a single precision float, the first step is to write ${\displaystyle x}$ as a normalized binary number:[15]
{\displaystyle {\begin{aligned}x&=\pm 1.b_{1}b_{2}b_{3}\ldots \times 2^{e_{x}}\\&=\pm 2^{e_{x}}(1+m_{x})\end{aligned}}}
where the exponent ${\displaystyle e_{x}}$ is an integer, ${\displaystyle m_{x}\in [0,1)}$, and ${\displaystyle 1.b_{1}b_{2}b_{3}\ldots }$ is the binary representation of the "significand" ${\displaystyle (1+m_{x})}$. Since the single bit before the point in the significand is always 1, it need not be stored. From this form, three unsigned integers are computed:[16]
• ${\displaystyle S_{x}}$, the "sign bit", is ${\displaystyle 0}$ if ${\displaystyle x}$ is positive and ${\displaystyle 1}$ negative or zero (1 bit)
• ${\displaystyle E_{x}=e_{x}+B}$ is the "biased exponent", where ${\displaystyle B=127}$ is the "exponent bias"[note 3] (8 bits)
• ${\displaystyle M_{x}=m_{x}\times L}$, where ${\displaystyle L=2^{23}}$[note 4] (23 bits)
These fields are then packed, left to right, into a 32-bit container.[17]
As an example, consider again the number ${\displaystyle x=0.15625=0.00101_{2}}$. Normalizing ${\displaystyle x}$ yields:
${\displaystyle x=+2^{-3}(1+0.25)}$
and thus, the three unsigned integer fields are:
• ${\displaystyle S=0}$
• ${\displaystyle E=-3+127=124=0111\ 1100_{2}}$
• ${\displaystyle M=0.25\times 2^{23}=2\ 097\ 152=0010\ 0000\ 0000\ 0000\ 0000\ 0000_{2}}$
these fields are packed as shown in the figure below:
### Aliasing to an integer as an approximate logarithm
If ${\displaystyle {\frac {1}{\sqrt {x}}}}$ were to be calculated without a computer or a calculator, a table of logarithms would be useful, together with the identity ${\displaystyle \log _{b}\left({\frac {1}{\sqrt {x}}}\right)=\log _{b}\left(x^{-{\frac {1}{2}}}\right)=-{\frac {1}{2}}\log _{b}(x)}$, which is valid for every base ${\displaystyle b}$. The fast inverse square root is based on this identity, and on the fact that aliasing a float32 to an integer gives a rough approximation of its logarithm. Here is how:
If ${\displaystyle x}$ is a positive normal number:
${\displaystyle x=2^{e_{x}}(1+m_{x})}$
then
${\displaystyle \log _{2}(x)=e_{x}+\log _{2}(1+m_{x})}$
and since ${\displaystyle m_{x}\in [0,1)}$, the logarithm on the right-hand side can be approximated by[18]
${\displaystyle \log _{2}(1+m_{x})\approx m_{x}+\sigma }$
where ${\displaystyle \sigma }$ is a free parameter used to tune the approximation. For example, ${\displaystyle \sigma =0}$ yields exact results at both ends of the interval, while ${\displaystyle \sigma ={\frac {1}{2}}-{\frac {1+\ln(\ln(2))}{2\ln(2)}}\approx 0.0430357}$ yields the optimal approximation (the best in the sense of the uniform norm of the error). However, this value is not used by the algorithm as it does not take subsequent steps into account.
The integer aliased to a floating point number (in blue), compared to a scaled and shifted logarithm (in gray).
Thus there is the approximation
${\displaystyle \log _{2}(x)\approx e_{x}+m_{x}+\sigma .}$
Interpreting the floating-point bit-pattern of ${\displaystyle x}$ as an integer ${\displaystyle I_{x}}$ yields[note 5]
{\displaystyle {\begin{aligned}I_{x}&=E_{x}L+M_{x}\\&=L(e_{x}+B+m_{x})\\&=L(e_{x}+m_{x}+\sigma +B-\sigma )\\&\approx L\log _{2}(x)+L(B-\sigma ).\end{aligned}}}
It then appears that ${\displaystyle I_{x}}$ is a scaled and shifted piecewise-linear approximation of ${\displaystyle \log _{2}(x)}$, as illustrated in the figure on the right. In other words, ${\displaystyle \log _{2}(x)}$ is approximated by
${\displaystyle \log _{2}(x)\approx {\frac {I_{x}}{L}}-(B-\sigma ).}$
### First approximation of the result
The calculation of ${\displaystyle y={\frac {1}{\sqrt {x}}}}$ is based on the identity
${\displaystyle \log _{2}(y)=-{\tfrac {1}{2}}\log _{2}(x)}$
Using the approximation of the logarithm above, applied to both ${\displaystyle x}$ and ${\displaystyle y}$, the above equation gives:
${\displaystyle {\frac {I_{y}}{L}}-(B-\sigma )\approx -{\frac {1}{2}}\left({\frac {I_{x}}{L}}-(B-\sigma )\right)}$
Thus, an approximation of ${\displaystyle I_{y}}$ is:
${\displaystyle I_{y}\approx {\tfrac {3}{2}}L(B-\sigma )-{\tfrac {1}{2}}I_{x}}$
which is written in the code as
i = 0x5f3759df - ( i >> 1 );
The first term above is the magic number
${\displaystyle {\tfrac {3}{2}}L(B-\sigma )={\mathtt {0x5F3759DF}}}$
from which it can be inferred that ${\displaystyle \sigma \approx 0.0450466}$. The second term, ${\displaystyle {\frac {1}{2}}I_{x}}$, is calculated by shifting the bits of ${\displaystyle I_{x}}$ one position to the right.[19]
### Newton's method
Relative error between direct calculation and fast inverse square root carrying out 0, 1, 2, 3, and 4 iterations of Newton's root-finding method. Note that double precision is adopted and the smallest representable difference between two double precision numbers is reached after carrying out 4 iterations.
With ${\displaystyle y}$ as the inverse square root, ${\displaystyle f(y)={\frac {1}{y^{2}}}-x=0}$. The approximation yielded by the earlier steps can be refined by using a root-finding method, a method that finds the zero of a function. The algorithm uses Newton's method: if there is an approximation, ${\displaystyle y_{n}}$ for ${\displaystyle y}$, then a better approximation ${\displaystyle y_{n+1}}$ can be calculated by taking ${\displaystyle y_{n}-{\frac {f(y_{n})}{f'(y_{n})}}}$, where ${\displaystyle f'(y_{n})}$ is the derivative of ${\displaystyle f(y)}$ at ${\displaystyle y_{n}}$.[20] For the above ${\displaystyle f(y)}$,
${\displaystyle y_{n+1}={\frac {y_{n}\left(3-xy_{n}^{2}\right)}{2}}}$
where ${\displaystyle f(y)={\frac {1}{y^{2}}}-x}$ and ${\displaystyle f'(y)=-{\frac {2}{y^{3}}}}$.
Treating ${\displaystyle y}$ as a floating-point number, y = y*(threehalfs - x/2*y*y); is equivalent to
${\displaystyle y_{n+1}=y_{n}\left({\frac {3}{2}}-{\frac {x}{2}}y_{n}^{2}\right)={\frac {y_{n}\left(3-xy_{n}^{2}\right)}{2}}.}$
By repeating this step, using the output of the function (${\displaystyle y_{n+1}}$) as the input of the next iteration, the algorithm causes ${\displaystyle y}$ to converge to the inverse square root.[21] For the purposes of the Quake III engine, only one iteration was used. A second iteration remained in the code but was commented out.[13]
### Accuracy
As noted above, the approximation is very accurate. The single graph on the right plots the error of the function (that is, the error of the approximation after it has been improved by running one iteration of Newton's method), for inputs starting at 0.01, where the standard library gives 10.0 as a result, and InvSqrt() gives 9.982522, making the relative difference 0.0017478, or 0.175% of the true value, 10. The absolute error only drops from then on, and the relative error stays within the same bounds across all orders of magnitude.
## History
William Kahan and K.C. Ng at Berkeley wrote an unpublished paper in May 1986 describing how to calculate the square root using bit-fiddling techniques followed by Newton iterations.[22] In the late 1980s, Cleve Moler at Ardent Computer learned about this technique[23] and passed it along to his coworker Greg Walsh. Greg Walsh devised the now-famous constant and fast inverse square root algorithm. Gary Tarolli was consulting for Kubota, the company funding Ardent at the time, and likely brought the algorithm to 3dfx Interactive circa 1994.[24][6]
Jim Blinn demonstrated a simple approximation of the inverse square root in a 1997 column for IEEE Computer Graphics and Applications.[25] Reverse engineering of other contemporary 3D video games uncovered a variation of the algorithm in Activision's 1997 Interstate '76.[26]
Quake III Arena, a first-person shooter video game, was released in 1999 by id Software and used the algorithm. Brian Hook may have brought the algorithm from 3dfx to id Software.[24] Copies of the fast inverse square root code appeared on Usenet and other forums as early as 2002 or 2003. Speculation arose as to who wrote the algorithm and how the constant was derived; some guessed John Carmack.[6] Quake III's full source code was released at QuakeCon 2005, but provided no answers. The authorship question was answered in 2006.[24]
In 2007 the algorithm was implemented in some dedicated hardware vertex shaders using field-programmable gate arrays (FPGA).[27]
## Subsequent improvements
### Magic number
It is not known precisely how the exact value for the magic number was determined. Chris Lomont developed a function to minimize approximation error by choosing the magic number ${\displaystyle R}$ over a range. He first computed the optimal constant for the linear approximation step as 0x5F37642F, close to 0x5F3759DF, but this new constant gave slightly less accuracy after one iteration of Newton's method.[28] Lomont then searched for a constant optimal even after one and two Newton iterations and found 0x5F375A86, which is more accurate than the original at every iteration stage.[28] He concluded by asking whether the exact value of the original constant was chosen through derivation or trial and error.[29] Lomont said that the magic number for 64-bit IEEE754 size type double is 0x5FE6EC85E7DE30DA, but it was later shown by Matthew Robertson to be exactly 0x5FE6EB50C7B537A9.[30]
Jan Kadlec reduced the relative error by a further factor of 2.7 by adjusting the constants in the single Newton's method iteration as well,[31] arriving after an exhaustive search at
conv.i = 0x5F1FFFF9 - ( conv.i >> 1 );
conv.f *= 0.703952253f * ( 2.38924456f - x * conv.f * conv.f );
return conv.f;
A complete mathematical analysis for determining the magic number is now available for single-precision floating-point numbers.[32][33]
### Zero finding
Intermediate to the use of one vs. two iterations of Newton's method in terms of speed and accuracy is a single iteration of Halley's method. In this case, Halley's method is equivalent to applying Newton's method with the starting formula ${\displaystyle f(y)={\frac {1}{y^{1/2}}}-xy^{3/2}=0}$. The update step is then
${\displaystyle y_{n+1}=y_{n}-{\frac {f(y_{n})}{f'(y_{n})}}=y_{n}\left({\frac {3+xy_{n}^{2}}{1+3xy_{n}^{2}}}\right),}$
where the implementation should calculate ${\displaystyle xy_{n}^{2}}$ only once, via a temporary variable.
## Notes
1. ^ A discussion is on the Chinese developer forum CSDN from 2000.[1]
2. ^ Use of the type long reduces the portability of this code on modern systems. For the code to execute properly, sizeof(long) must be 4 bytes, otherwise negative outputs may result. Under many modern 64-bit systems, sizeof(long) is 8 bytes. The more portable replacement is int32_t.
3. ^ ${\displaystyle E_{x}}$ should be in the range ${\displaystyle [1,254]}$ for ${\displaystyle x}$ to be representable as a normal number.
4. ^ The only real numbers that can be represented exactly as floating point are those for which ${\displaystyle M_{x}}$ is an integer. Other numbers can only be represented approximately by rounding them to the nearest exactly representable number.
5. ^ Since ${\displaystyle x}$ is positive, ${\displaystyle S_{x}=0}$.
## References
1. ^ "Discussion on CSDN". Archived from the original on 2015-07-02.
2. ^ Munafo, Robert. "Notable Properties of Specific Numbers". mrob.com. Archived from the original on 16 November 2018.
3. ^ a b Ruskin, Elan (2009-10-16). "Timing square root". Some Assembly Required. Archived from the original on 2021-02-08. Retrieved 2015-05-07.
4. ^
5. ^ Blinn 2003, p. 130.
6. ^ a b c d Sommefeldt, Rys (2006-11-29). "Origin of Quake3's Fast InvSqrt()". Beyond3D. Retrieved 2009-02-12.
7. ^ "quake3-1.32b/code/game/q_math.c". Quake III Arena. id Software. Archived from the original on 2020-08-02. Retrieved 2017-01-21.
8. ^ Eberly 2001, p. 504.
9. ^ Lomont 2003, p. 1.
10. ^
11. ^ Lomont 2003, p. 3.
12. ^ McEniry 2007, p. 2, 16.
13. ^ a b Eberly 2001, p. 2.
14. ^ Fog, Agner. "Lists of instruction latencies, throughputs and micro-operation breakdowns for Intel, AMD and VIA CPUs" (PDF). Retrieved 2017-09-08.
15. ^ Goldberg 1991, p. 7.
16. ^ Goldberg 1991, pp. 15–20.
17. ^ Goldberg 1991, p. 16.
18. ^ McEniry 2007, p. 3.
19. ^ Hennessey & Patterson 1998, p. 305.
20. ^ Hardy 1908, p. 323.
21. ^ McEniry 2007, p. 6.
22. ^
23. ^ Moler, Cleve. "Symplectic Spacewar". MATLAB Central - Cleve's Corner. MATLAB. Retrieved 2014-07-21.
24. ^ a b c Sommefeldt, Rys (2006-12-19). "Origin of Quake3's Fast InvSqrt() - Part Two". Beyond3D. Retrieved 2008-04-19.
25. ^ Blinn 1997, pp. 80–84.
26. ^ Peelar, Shane (1 June 2021). "Fast reciprocal square root... in 1997?!".
27. ^ Middendorf 2007, pp. 155–164.
28. ^ a b Lomont 2003, p. 10.
29. ^ Lomont 2003, pp. 10–11.
30. ^ Matthew Robertson (2012-04-24). "A Brief History of InvSqrt" (PDF). UNBSJ.
31. ^ Kadlec, Jan (2010). "Řrřlog::Improving the fast inverse square root" (personal blog). Retrieved 2020-12-14.
32. ^
33. ^ Muller, Jean-Michel (December 2020). "Elementary Functions and Approximate Computing". Proceedings of the IEEE. 108 (12): 2146. doi:10.1109/JPROC.2020.2991885. ISSN 0018-9219.
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2023-02-04 00:50:09
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http://experiment-ufa.ru/derivative_of_cos(90)
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# Derivative of cos(90)
## Derivative of cos(90). Simple step by step solution, to learn. Simple, and easy to understand, so dont hesitate to use it as a solution of your homework.
If it's not what You are looking for type in the derivative calculator your own function and let us solve it.
## Derivative of cos(90):
(cos(90))'0`
The calculation above is a derivative of the function f (x)
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2018-06-23 17:23:26
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https://socratic.org/questions/what-is-the-inverse-of-y-e-x-1-1
|
# What is the inverse of y= e^(x-1)-1 ?
Dec 7, 2015
${f}^{- 1} \left(x\right) = \ln \left(x + 1\right) + 1$
#### Explanation:
To compute the inverse, you need to follow the following steps:
1) swap $y$ and $x$ in your equation:
$x = {e}^{y - 1} - 1$
2) solve the equation for $y$:
... add $1$ on both sides of the equation...
$x + 1 = {e}^{y - 1}$
... remember that $\ln x$ is the inverse function for ${e}^{x}$ which means that both $\ln \left({e}^{x}\right) = x$ and ${e}^{\ln x} = x$ hold.
This means that you can apply $\ln \left(\right)$ on both sides of the equation to "get rid" of the exponential function:
$\ln \left(x + 1\right) = \ln \left({e}^{y - 1}\right)$
$\ln \left(x + 1\right) = y - 1$
... add $1$ on both sides of the equation again...
$\ln \left(x + 1\right) + 1 = y$
3) Now, just replace $y$ with ${f}^{- 1} \left(x\right)$ and you have the result!
So, for
$f \left(x\right) = {e}^{x - 1} - 1$,
the inverse function is
${f}^{- 1} \left(x\right) = \ln \left(x + 1\right) + 1$
Hope that this helped!
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2019-12-11 07:03:03
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https://brilliant.org/problems/simple-isnt-it-7/
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# Simple isn't it? #7
A group of friends from BRILLIANT decide to go for a bungee jumping camp. The second one to jump is Swapnil. He jumps from the top of a cliff of height $$H$$. He performs a damped oscillatory motion along the vertical motion. The first time he reaches at the lowest level ,i.e, $$height=0m$$ above the ground. Then he goes up to a certain height. Similar type of motion goes on until an equilibrium state is obtained at height $h=\frac{51H}{200}$.
Find the maximum velocity obtained during the motion.
The maximum velocity is given by: $$\frac{a}{b}\sqrt{\frac{Hg}{c}}$$
Find $$a+b+c$$
Details and Assumptions
• Nothing bad happens to Swapnil.
• Consider Swapnil to be a point sized particle.
This problem is of this set.
×
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2017-05-27 15:53:57
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https://yossadh.github.io/posts/2019/02/linear-regression-grace/
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# Plotting business: Automated linear regression with Grace
Published:
What software do you use to plot?
Like most people my first experience was with Excel. I remember the settings were quite confusing and not intuitive (this was Excel 2000/2003, no idea about current version). Then there are commercial softwares like Origin, which I used for here and there. It is quite user-friendly, but 1) I try to avoid pricy software packages when I can, and 2) commercial packages usually only run on Windows and I haven’t had main Windows workstation in years. My experimental colleagues use mostly GraphPad, and the graphs look nice, but I never used it for the same reasons as Origin.
A comment about Google Sheets: one would expect it will be similar to Excel, but I’m pleasantly surprised that it is easy to use and yields pretty graphs. I use this for simple charts that do not need heavy customisation/annotations, e.g. histogram.
Most recently I have learned to use the myriad of Python packages: matplotlib, holoviews and the like. They are indeed powerful, pretty, and customisability is certainly there as far as your Python fu allows. But the learning curve is pretty high. Even when generating simple plots, I have to look up stuff again, even though I already have a previous script as template.
So, I found myself keep going back to Grace, an ancient(?) and arcane plotting software I first learned in undergraduate days when I first encountered a Linux machine. Ok I always thought it’s ancient (like 70s-80s) because of how the GUI looks, but it was released in 1990s. Anyway, its graphs have a sort of signature look to it, and one can still see it in journal papers, especially molecular dynamics papers.
I can think of a few reasons why Grace sticks. First, you can get a plot very quickly from a plain-text file. In matplotlib, you have to import the data first into pandas dataframe and whatnot. Second, the plot file itself is a plain-text file containing the parameters and the data. Plain text means that it can be modified with the bash arsenal of text manipulation. Arguably, matplotlib is the same in this regard but it is a little different. The matplotlib .py script would be the instructions to construct the graph, while the Grace .agr file have the parameters and their values there (although it’s also possible to to save Grace instruction file – this is called the batch file). For holoviews for example, I found myself looking up for the correct commands/instructions to set some parameters, while in Grace I can just go to to the parameter in question and change its value.
Here I will demonstrate how I use Grace and some tips and tricks. Suppose you have data.dat that you want to plot:
# if you don't have some data handy, use this random number generator
# generates 10 numbers less than 100
for i in {1..10}; do echo $i$(expr $RANDOM % 100); done > data.dat # cat data.dat 1 11 2 3 3 29 4 87 5 15 6 38 7 6 8 55 9 7 10 32 Simply call Grace to plot it: # Grace with GUI xmgrace data.dat And you will see a meh-looking plot. But the power of Grace is in the script automation. Save this plot as data.agr. Here is fit.par which will do linear regression and plot the regression plot: # cat fit.par with g0 view ymin 0.45 view ymax 0.85 s0 symbol 3 s0 symbol size 0.400000 s0 line type 0 # regression formula fit formula "y = a0 + a1*x" fit with 2 parameters fit prec 1e-5 # run regression, 100 iterations nonlfit(s0,100) # duplicate data from original data (s0) to s1 copy s0 to s1 s1 symbol 0 s1 line type 1 s1 line color 7 s1 type xy # overwrite y to make regression line s1.y = a0 + a1*x autoscale Apply fit.par: # Grace with command-line interface grace data.agr -param fit.par -saveall data.fit.agr -hardcopy -noprint > data.fit.log You will be glad when you have 15 plots to do linear regression on like I do. I guess you can do the clicking around on the GUI 15 times but what will you do if you have 100 plots? One more thing I needed was to put the R2 values in the graphs. I did this in a very roundabout way (please tell me if you have a more elegant solution): • Annotate each of the 15 graphs (I have put them in one file, plot.agr) with textboxes containing the strings “corr1”, …, “corr15” • Extract R-value from data.fit.log and calculate R2 bash \rm correlation.dat for i in {1..15}; do grep -H Correlation data$i.fit.log » correlation.dat done awk ‘{printf %.2f\n”, $3^2}’ correlation.dat > corr_squared.dat • Make a dictionary corr.dict such that ‘corr1’ corresponds to first value of R2, and so on # cat corr.dict corr1 0.71 ... corr15 0.80 • Replace plot.agr (the 15 graphs) consulting the dictionary (remember what I said about plain-text .agr being amenable to text manipulation?): awk 'NR == FNR { rep[$1] = \$2
next
}
{
for (key in rep)
gsub(key, rep[key])
print
}' corr.dict plot.agr > plot_check.agr
`
Grace is powerful, but unfortunately the documentation, especially the scripting part, is a bit sparse. Hopefully that will improve!
Tags:
Categories:
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2020-01-18 19:45:12
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https://www.sobyte.net/post/2022-08/c-volatile/
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When learning C language there is a strange keyword volatile, what exactly is the use of this?
## volatile and the compiler
First look at a piece of code like this.
1 2 3 4 5 6 7 int busy = 1; void wait() { while(busy) { ; } }
Compile it and note that O2 optimization is used here:
Let’s take a closer look at this generated assembly.
1 2 3 4 5 6 7 8 9 wait: mov eax, DWORD PTR busy[rip] .L2: test eax, eax jne .L2 ret busy: .long 1
As you can see, the decision to jump out of the loop is made by checking the eax register, but not by checking the real content of the memory where the variable busy is located.
Note that the optimization is correct for this code, but the problem is that if there is other code that modifies the variable busy, then the optimization will cause the other code to modify the variable busy in such a way that it will not take effect at all, like this.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 int busy = 1; // This function is executed in thread A void wait() { while(busy) { ; } } // This function is executed in thread B void signal() { busy = 0; }
If the machine instruction corresponding to the while loop in the wait function simply reads from a register, then even if thread B’s signal function modifies the busy variable, it will not allow the wait function to jump out of the loop.
If you use the volatile modifier on the busy variable, the resulting instruction would look like this.
1 2 3 4 5 6 7 8 wait: .L2: mov eax, DWORD PTR busy[rip] test eax, eax jne .L2 ret busy: .long 1
Note that at this point the paragraph L2, each time reads the data from the memory where the busy variable is located and stores it in eax, then goes to the judgment, so as to ensure that the latest value of the busy variable is read every time.
In fact, you can treat the register eax as the cache of the memory where the busy is located. When the cache (register) and the data in memory are the same, there is no problem, but when the cache and the data in memory are not the same (that is, the memory has been updated but the cache still holds the old data), the program often runs unexpectedly.
In addition to the multi-threaded example, there is also a category of signal handler and hardware modification of the variable (often encountered when interacting with hardware in C), if the compiler generates instructions like the one at the beginning of the article then the waiting thread will not detect the signal handler or hardware modification of the variable.
So here we need to tell the compiler: “Don’t be clever, don’t just read data from registers, this variable may have been modified elsewhere, get the latest data from memory when using it”.
Now it’s time to briefly summarize that volatile only prevents the compiler from trying to optimize read operations on variables.
Be sure to note that volatile only ensures the visibility of variables, but has nothing halfway to do with atomic access to variables, which are two completely different tasks.
Suppose there is a very complex struct struct foo.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 struct data { int a; int b; int c; ... }; volatile struct data foo; void thread1() { foo.a = 1; foo.b = 2; foo.c = 3; ... } void thread2() { int a = foo.a; int b = foo.b; int c = foo.c; ... }
You just use volatile to modify the variable foo just to ensure that when the variable is modified by thread1 we can read the latest value in thread2, but this does not solve the problem of multi-threaded concurrent reads and writes that require atomic access to foo.
Ensuring atomic access to variables generally uses locks, and when locks are used, the locks themselves include the ability to provide volatile, i.e., ensure visibility of the variable, so there is no need to use volatile when locks are used.
## volatile and memory order
Some of you may be thinking that if the variable I want to modify with volatile is not that complicated and is just an int, like this.
1 volatile int busy = 0;
Is it possible for thread A to read the busy variable, thread B to update the busy variable, and then perform a specific action when A detects a change in the busy? Since the volatile modification ensures that the busy is read from memory every time, it should be possible to use it that way.
However, computers may be relatively simple conceptually, but they are complex in engineering practice.
We know that since the speed difference between CPU and memory is very large, there is a layer of cache between CPU and memory, and CPU does not actually read memory directly. The existence of cache will complicate the problem, and limited to space and the topic of this article here will not be expanded.
In order to optimize memory reading and writing, the CPU may reorder the instructions for memory reading and writing operations. The consequence is: suppose the Nth line of code and the N+1th line of code are executed successively in Thread 1, but Thread 2 seems to be the N+1th line of code that takes effect first, assuming the initial value of X is 0 and the initial value of Y is 1.
1 2 3 // Thread 1 Thread 2 X = 10 if (!busy) busy = 0; Y = X;
When thread 2 reads the value of X after detecting that BUSY is 0, the value of X read at this point may be 0.
To solve this problem, what we need is not volatile, which does not solve the reordering problem, but a memory barrier.
A memory barrier is a class of machine instructions that limits the memory operations that the processor can perform before and after the barrier instruction, ensuring that no reordering problems occur.
The effect of a memory barrier still covers the functionality provided by volatile, so volatile is not needed.
As you can see, we almost always do not use the volatile keyword in a multi-threaded environment.
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2022-08-08 03:48:01
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